Researchers often run algorithms designed for quantum computers on classical computers that can simulate their behavior before executing them on actual quantum hardware.

Using quantum circuit simulators, such as the IBM Quantum Platform Composer, enables prediction and validation of potential results while reducing the computational time and cost often associated with running algorithms on quantum hardware.

Then, this raises the question: Why build quantum computers if you can simulate them?

High-performance classical computers are valuable for simulating smaller quantum circuits or programs. However, in practical use cases that are too complex and resource-intensive for classical computers to handle, quantum computers remain necessary.

This article explores the current thresholds and limitations of quantum computers and quantum circuit simulators and when it is appropriate to use either.

What is a quantum circuit simulator?

A quantum circuit simulator is a software platform accessed on a classical computer (i.e., a laptop) that allows you to run quantum circuits, or software programs that can run on a quantum computer, as if they were running on a quantum computer.

Popular web-based quantum circuit simulators include IBM Quantum Circuit Composer, Cirq, and BlueQubit Simulator. Popular libraries include the cuStateVec library in the NVIDIA cuQuantum SDK and the PennyLane SDK.

Quantum simulator vs. quantum circuit simulator

A common misconception is that quantum circuit simulators are quantum simulators, but they are fundamentally different.

A quantum simulator is a broad term for a tool that models complex physical systems. For example, a quantum simulator is used to model the atoms of a chemical molecule that scientists use to research new materials. Quantum computers are often used as quantum simulators.

In contrast, a quantum circuit simulator models the behavior of a quantum computer, including its state, on a classical computer using well-defined mathematical logic. For example, a quantum circuit simulator can model a result similar to that a quantum computer would produce when acting as a quantum simulator of a chemical molecule.

A quantum simulator can be a quantum computer, but a quantum circuit simulator cannot.

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Limitations of quantum circuit simulation

Quantum circuit simulators face limitations as circuit sizes (in qubits and gates) grow, because they require excessive data storage and the mathematical calculations they perform to model quantum computers become too complex.

At present, quantum circuit simulators can handle only a maximum of 30–50 qubits and are unable to fully replicate even today’s cloud-accessible quantum computers of 100–200 qubits. To run a useful practical algorithm, at least 100 qubits are necessary [4].

Major memory requirements

First, classical computers are limited by random access memory (RAM) available to store all possible quantum states.

A state vector circuit simulator, the most common implementation of a quantum circuit simulator, stores the quantum state of each qubit as a state vector.

The state vector space grows exponentially with the number of qubits, making it too large for classical computers to handle. If you are interested in a deeper dive into quantum states, please refer to this article.

Each state vector contains two complex numbers representing the probabilities that the qubit is in states 0 and 1. Therefore, a system requires two complex numbers per additional qubit.

Each complex number requires 16 bytes of RAM. Since each qubit requires a state vector of two complex numbers, the state vector for each qubit requires 32 bytes of RAM. A simple formula to calculate the required RAM to simulate a system is 2^(N+4) bytes, where N is the number of qubits [1].

The RAM requirements for a state vector circuit simulator are manageable with fewer qubits, but are impractical as the number of qubits scales.

Two qubits require 64 bytes, which is the equivalent of a 64-character text message.

# RAM in bytes for two qubits

2^(N+4) with N as the number of bytes
2^(2+4)
2^(6)
64 bytes

Thirty qubits require 17,179,869,184 bytes, or 17 gigabytes of RAM, which is the equivalent of the lowest-tier MacBook Pro.

2^(30+4) = 2^34 = 17,179,869,184 bytes or 17 gigabyes

One hundred qubits require 2.028241 x 10³¹ bytes or 2.02824096 × 10²² gigabytes, which is more than all of the RAM space available in the world. A state vector circuit simulator could not replicate even the largest quantum processor currently available to users.

2^(100+4) = 2^104 = 2.028241 x 10^31 bytes or 2.02824096 × 10^22 gigabytes

The development of quantum computers remains necessary because classical computers cannot simulate them at scale, particularly for future use cases requiring hundreds or thousands of qubits.

Complicated mathematics

The complexity of the mathematical calculations also grows exponentially with the number of qubits and gates (logic operations applied to qubits).

In state vector simulators, qubits and gates are represented as matrices, requiring complex multiplication as more are added.

As an example, here is a matrix of two qubits, where the first qubit is in the initial state of |1> and the second is in the ground state |0>:

              ⎡ 0·1 ⎤   ⎡ 0 ⎤
              ⎢ 0·0 ⎥   ⎢ 0 ⎥
|1⟩ ⊗ |0⟩  =  ⎢ 1·1 ⎥ = ⎢ 1 ⎥ = |10⟩
              ⎣ 1·0 ⎦   ⎣ 0 ⎦

Here is the matrix of a controlled NOT (CNOT gate), which changes the state of the target (second) qubit to the opposite of the control qubit’s state only if the control qubit’s state is |1⟩.

       ⎡ 1  0  0  0 ⎤
CNOT = ⎢ 0  1  0  0 ⎥
       ⎢ 0  0  0  1 ⎥
       ⎣ 0  0  1  0 ⎦ 

To apply a CNOT gate to the two qubits, the following matrix multiplication is applied.

       ⎡ 1  0  0  0 ⎤ ⎡ 0 ⎤   ⎡ 0 ⎤
CNOT = ⎢ 0  1  0  0 ⎥ ⎢ 0 ⎥ = ⎢ 0 ⎥ = |11⟩
       ⎢ 0  0  0  1 ⎥ ⎢ 1 ⎥   ⎢ 0 ⎥
       ⎣ 0  0  1  0 ⎦ ⎣ 0 ⎦   ⎣ 1 ⎦

As the number of qubits and gates grows, classical computers struggle to keep up with the matrix multiplication involved. This cost grows exponentially, described by O(m·2^(2N)), where N is the number of qubits and m is the number of gates [1].

Types of quantum circuit simulation in practice

Various types of quantum simulation tools exist but the same code is used to model a physical system on a quantum simulator and to show the state of a quantum computer using a quantum circuit simulator.

The following Python code snippets, using the PennyLane SDK to model two hydrogen atoms separated by 1.4 Bohr, representing the most stable bond to form a hydrogen molecule, require four qubits and can either run on a quantum computer or a quantum circuit simulator.

import pennylane as qml
from pennylane import numpy as np

# Describes two hydrogen atoms that are -1.4 Bohr apart

symbols = [”H”, “H”]
coords  = np.array([[0.0, 0.0, 0.0],
                    [0.0, 0.0, 1.4]])

# Translates the hydrogen molecule into something a quantum computer understands
# H represents the total energy system of the molecule
# n represents how many qubits the molecule needs

H, n = qml.qchem.molecular_hamiltonian(symbols, coords, basis=”sto-3g”, method=”dhf”)

This code runs the Variational Quantum Eigensolver, a popular algorithm for finding the ground state of physical systems, in this case, the ground state of a hydrogen molecule.

def prepare(theta):
    qml.BasisState(start, wires=range(n))
    qml.DoubleExcitation(theta, wires=[0, 1, 2, 3])

# measures the energy of the molecule
@qml.qnode(qc)                         
def energy(theta):
    prepare(theta)
    return qml.expval(H)

# measures the state of the molecule
@qml.qnode(qc)                          
def state(theta):
    prepare(theta)
    return qml.probs(wires=range(n))

# Uses the Variational Quantum Eigensolver (VQE) to turn 
# the different parameters until the energy is as low as it goes 
theta = np.array(0.0, requires_grad=True)
opt = qml.GradientDescentOptimizer(stepsize=0.4)
for _ in range(40):
    theta = opt.step(energy, theta)

# The ground state that a quantum simulator or quantum circuit simulator finds
E_found = float(energy(theta))
E_exact = float(np.linalg.eigvalsh(qml.matrix(H, wire_order=range(n)))[0])

The main difference in the code is that these lines specify which type of “simulator” we would use, choosing either an actual quantum computer or a quantum circuit simulator running on a classical computer.

# Defines the simulator that we would use (choose one or the other)

# 1. uses a IonQ Forte1 quantum computer that is accessible through Amazon Web Services (AWS)
device_arn = “arn:aws:braket:us-east-1::device/qpu/ionq/Forte-1”
qc = qml.device(”braket.aws.qubit”, device_arn=device_arn, wires=n, shots=1000)

# OR 2. uses the default built-in quantum circuit simulator that uses a classical computer
qc = qml.device(”default.qubit”, wires=n)

Running the full code on different types of simulators follows a similar process but can yield different results and requires different resources.

Running this example on an IonQ Forte1 quantum computer via Amazon Web Services (AWS) Braket would require more than $74.

The current on-demand rate is $0.30 per task + $0.08 per shot per task (the number of times a task is run). With six separate tasks in the full script and an optimal of 150 shots for a smaller VQE circuit, the estimated cost is nearly $74 [2].

Rate for on-demand access to IonQ Forte1 device: $0.30 / task + $0.08 / shot per tasks 

Number of tasks: 6
Number of (optimal shots); 150
($0.30 * 6) + ($0.08 * 6 * 150)
$1.80 + $72.00 = $73.80

A dedicated quantum computer could execute the program in seconds to minutes, but dedicated reserved time of an IonQ Forte1 would cost $7,000 per hour on AWS. Most developers would opt for shared cloud quantum resources, which means quantum circuit execution can take hours due to queuing hundreds or thousands of requests, as shown on the IBM Quantum Platform status tracker.

Since I did not want to pay $74, I “cheated” and used DM1, an AWS simulator that includes noise, or disturbances commonly encountered in quantum computers. A simulator that integrates noise simulates a quantum computer more closely than ones that do not, such as a universal state vector simulator, the most common implementation of a quantum circuit simulator.

Using the DM1 simulator saved a considerable amount of time and money compared to a real quantum computer; it cost $0.0225 and took 18 seconds to run.

# uses DM1 AWS quantum simulator as device to run the circuit
device_arn = “arn:aws:braket:::device/quantum-simulator/amazon/dm1”

Modeling H2 uses 4 qubits.

GROUND-STATE ENERGY
  ideal (no noise)  : -1.13728 Hartree
  DM1 (with noise)  : -1.08274 Hartree

THE MOLECULE’S QUANTUM STATE (noisy)
    0011   probability  0.80%
    0100   probability  1.70%
    1000   probability  1.40%
    1100   probability 92.30%
    1101   probability  1.90%
    1110   probability  1.50%
    1111   probability  0.20%

In general, since the circuit requires only four qubits, all quantum circuit simulators should produce a similar result.

Next, I ran the result using the default built-in state vector quantum circuit simulator in the PennyLane SDK, which is free and provides instant results.

A state vector simulator returns the same result each time because it applies deterministic mathematical operations to the state vector based on the gates in the circuit. The next section explains how using predetermined mathematical logic in quantum circuit simulation limits its capabilities.

Compared to the DM1 result, the result using the default state vector quantum circuit simulator in the PennyLane SDK was more precise, with fewer chances of varying quantum states, due to the lack of noise:

Modeling H2 uses 4 qubits.

GROUND-STATE ENERGY
  quantum circuit simulator found: -1.13728 Hartree
  known exact answer: -1.13728 Hartree

THE MOLECULE’S QUANTUM STATE
  (each row is one way the 2 electrons can sit in the 4 orbital-slots)
    0011   probability  1.27%
    1100   probability 98.73%

Researchers working with circuits that have fewer qubits, such as this example, benefit from more accessible, faster, and cheaper simulations rather than running circuits directly on quantum hardware. However, as their circuits grow, they will encounter limitations with quantum circuit simulators.

Conclusion

High-performance classical computers are valuable and effective for simulating smaller quantum circuits or programs, like the four-qubit example in the article. Using the built-in state vector simulator returned an exact ground-state energy instantly and for free, while running the same circuit on an IonQ Forte1 would have cost nearly $74.

However, classical simulation becomes too mathematically complex and resource-intensive as the number of qubits in consumer-accessible quantum computers grows. At 30 qubits, a simulator already requires 17 gigabytes of RAM; at 100 qubits, it would require more RAM than exists in the world.

So, why build quantum computers if you can simulate them? For practical use cases that will require hundreds or thousands of qubits, classical simulation is too complex and resource-intensive, and quantum computers remain necessary.

Additional Resources

1. Xu, X., Lee, J. S., & Lim, Y. S. (2023). A Herculean task: Classical simulation of quantum computers (arXiv:2302.08880). arXiv. https://arxiv.org/abs/2302.08880

2. Bisicchia, G., Bocci, A., Pimentel, E., & Brogi, A. (2026). How many shots are enough for a quantum circuit? (arXiv:2606.16965). arXiv. https://arxiv.org/abs/2606.16965

3. McGuffin, M. J., Robert, J.-M., & Ikeda, K. (2025). How to write a simulator for quantum circuits from scratch: A tutorial (arXiv:2506.08142). arXiv. https://arxiv.org/abs/2506.08142

4. Preskill, J. (2018). Quantum computing in the NISQ era and beyond (arXiv:1801.00862). arXiv. https://arxiv.org/abs/1801.00862

Over 90% of developers who create software for classical computers use AI tools to help them code. But, how about for quantum programming?

While there is no direct data on AI adoption in quantum programming, recently, numerous open and closed-access quantum-specific tools have become available for developing quantum algorithms:

Open access:

• Conductor Quantum Coda

• Qiskit Code Assistant (local only, uses LLM model Qwen 2.5)

• General-purpose AI tools (ChatGPT, Claude, Google Colab notebook with Gemini), as 90% of open-source quantum software developers use general-purpose languages like Python.

Closed access:

• Hiverge (partnership with Quantinuum)

• Classiq Quantum Agents

Quantum AI tools for managing quantum computing workflows, including error correction, are now emerging, such as NVIDIA Ising.

In the first part of this series, this article analyzes the effectiveness of using open-access, general-purpose AI tools to develop simple quantum algorithms for educational purposes.

For the purposes of this article, I tested Conductor Quantum Coda, Claude, ChatGPT, Qiskit Code Assistant, and Gemini in a Google Colab notebook.

Simplest prompt statement: Create a Bell state preparation circuit

My goal was to test the simplest possible prompt on each AI tool to evaluate its capacity as an educational tool.

A Bell state preparation circuit was the simplest value-add circuit I could think of, as it consists of only two components. It clearly demonstrates the foundation of quantum computers, that qubits can act as a single system composed of hundreds or thousands of bits.

I chose an open-ended prompt:

Create a Bell state preparation circuit

What is a Bell State preparation circuit?

I expected any response from the AI tool to coherently explain a Bell state and a Bell state preparation circuit:

A Bell state refers to when two qubits, fundamental units of quantum computing, are experiencing the maximum possible entanglement. Entanglement refers to when qubits remain connected even when physically far away by vast distances.

In other words, a Bell state preparation circuit is a quantum program that demonstrates that two qubits remain connected even when physically separated.

A Hadamard gate (symbolized by the box with an H), applied to the qubit x, puts the qubit x in an equal superposition, or chance that the state is either |0> or |1>.

Subsequently, a CNOT gate (symbolized by the black dot connected to a target circle), set to control qubit x and applied to qubit y, changes the state of qubit y to match the state of qubit x. This demonstrates that the state of qubit y is correlated with qubit x.

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Key takeaways in testing the AI tools

1. IBM Qiskit is the default software development stack.

Conductor Quantum Coda, Claude, and Gemini returned the same Python code using the Qiskit SDK for a Bell state preparation circuit, while ChatGPT and Qiskit Code Assistant returned a different variation of Qiskit.

Qiskit is an IBM software development kit (SDK) that enables developers to write quantum circuits in Python. Qiskit is the most widely used quantum software development platform, with nearly 70 percent of open-source quantum developers using it, making it an obvious choice for AI tools.

Conductor Quantum Coda offered an option to select code that integrates with other popular SDKs and frameworks, including NVIDIA CUDA-Q, Amazon Braket, Google Cirq, PennyLane, Rigetti PyQuil, and OpenQASM 3.0. Other AI tools default to Qiskit with no toggle options.

2. (Somewhat) code standardization

Given the circuit’s simplicity, it was expected that code within the same framework would be similar.

The Python code using the Qiskit SDK that most AI tools returned was:

from qiskit import QuantumCircuit

qc = QuantumCircuit(2, 2)
qc.h(0)
qc.cx(0, 1)
qc.measure([0, 1], [0, 1])

• qc = QuantumCircuit(2, 2) — creates a quantum circuit with two qubits and two classical bits used for state measurement

• qc.h(0) — applies a Hadamard gate on the first qubit

• qc.cx — applies a CNOT gate to the second qubit depending on the first qubit’s state, meaning the first qubit acts as the control and the second as the target.

• qc.measure([0,1,[0,1]) — measures the current state of the qubit.

ChatGPT returned correct, but slightly different Python code:

from qiskit import QuantumCircuit

qc = QuantumCircuit(2)

qc.h(0)
qc.cx(0, 1)

qc.draw(”mpl”)

The key differences from the ChatGPT version were that it eliminated the two classical qubits used for measurement and displayed a circuit diagram instead of performing a measurement.

Qiskit Code Assistant, the AI agent developed directly by IBM, combined both approaches and took it a step further by optimizing it for quantum hardware.

• qc = transpile(qc, basis_gates=[’u3’, ‘cx’]) — The transpilation process rewrites an input circuit to optimize it for a specific quantum device, because not all quantum computers support all gates. This particular line converts the circuit into another that uses a U3 gate, a generic single-qubit rotation with three Euler angles, instead of a Hadamard gate. However, it appears the local version of Code Assistant I have access to is outdated, as the U3 gate has already been deprecated.

from qiskit import QuantumCircuit, transpile

def create_bell_state_circuit():
    qc = QuantumCircuit(2, 2)
    qc.h(0)
    qc.cx(0, 1)
    qc.measure(range(2), range(2))
    return qc

if __name__ == “__main__”:
    qc = create_bell_state_circuit()
    print(qc.draw(output=’text’))
    qc = transpile(qc, basis_gates=[’u3’, ‘cx’])
    print(”\nTranspiled circuit:\n”)
    print(qc.draw(output=’text’))

3. Only Coda supports running directly on a quantum computer.

Conductor Quantum Coda was the only tool that supported in-app deployment of a circuit to a cloud service that connected to a quantum computer. This feature simplified the process by removing the need to create, upload, and run a program file as a workflow on a quantum cloud platform.

Coda was the only tool that estimated the number of resources needed, including qubits, depth (the number of times steps, or the time it takes to execute one gate, needed to execute all gates in a quantum circuit), and gates (the number of operations).

Despite this, it did not recognize that the circuit was small enough to avoid the need for expensive quantum hardware, and the result could have easily been simulated on a classical computer.

It recommended the default quantum hardware to me (AQT IBEX Q1). I was not going to pay $20.30 to run a simple circuit that I could on a classical computer!

And, I did run the AI-generated circuit on their built-in classical simulator for free, which was more than sufficient. The circuit state has a 50% chance of being |00> or |11>.

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Although they do not support direct deployment, Gemini and Qiskit Code Assistant were not merely chat interfaces and could be used directly in code editors. This allows for easy code editing while utilizing AI.

I used Gemini while writing Python code in a Google Colab notebook.

I loaded Qiskit Code Assistant while writing Python code in the Visual Studio Code desktop editor.

4. (Wide) range of explanations of code and concepts.

The vast differences were found in the explanations of the code and the concept of a Bell state and a Bell state preparation circuit.

Claude and Conductor Quantum Coda provided extensive written explanations of their Bell state preparation circuits, while Gemini and ChatGPT were more succinct. Qiskit Code Assistant did not provide any written explanation; only diagrams of the circuits shown in Point 2 above were provided. Only ChatGPT, Claude, and Qiskit Code Assistant provided circuit diagrams.

For example, ChatGPT provided a simple line and text drawing of a Bell State preparation circuit.

|0⟩ ── H ──■──
           │
|0⟩ ───────X──

While Claude provided a more in-depth visualization using linear algebra.

Claude describes the diagram as:

Start with both qubits in |0⟩. Apply a Hadamard gate to qubit 0, which puts it into an equal superposition: H|0⟩ = (|0⟩ + |1⟩)/√2. The two-qubit state becomes (|00⟩ + |10⟩)/√2.

Then apply a CNOT with qubit 0 as control and qubit 1 as target. CNOT flips the target whenever the control is |1⟩, so |00⟩ stays |00⟩ and |10⟩ becomes |11⟩. The final state is (|00⟩ + |11⟩)/√2 — the Φ⁺ Bell state.

My recommendation

For simple circuits for educational purposes:

Conductor Quantum Coda is the most quantum-native AI tool, but it may be too advanced for beginner quantum developers who are not yet prepared to deploy or run programs on a quantum computer.

Gemini and Qiskit Code Assistant are valuable tools for developers who want to edit code while using AI as they write.

Other general-purpose AI tools, like Claude and ChatGPT, are designed mainly for chat interactions, where the user is interested in exploring quantum programming and visualizations, but does not plan to modify or eventually run the code.

In future parts, I’ll analyze the results with more intermediate and advanced circuit requests. I hypothesize that a clearer distinction between code and responses will emerge for more ambiguous algorithm requests.

This week’s roundup is too long for email, so please check it out on the Substack app.

This week, I’ve been a bit consumed with the “cryptography” side of research, so this edition is shorter.

In case you’re wondering: several blockchain/DeFi applications and protocols have been attacked due to non-quantum-related vulnerabilities, resulting in multi-million-dollar losses:

• Drift Protocol: $285 million loss

• KelpDAO rsETH token: $292 million loss

• Volo Protocol: $3.5 million loss

• Litecoin: $600,000 potential loss, blockchain reverted to the previous version before the hack

• Scallop Protocol: $142,000

The numerous non-quantum hacks and vulnerabilities in blockchain and many other industries raise concerns about whether anyone is truly prepared for post-quantum migration. Azeem Khan, CEO of Miden, puts it in his weekly reflection:

In other words, how can we prepare for the post-quantum world when digital security is so fragile in our current world? It’s an excellent food for thought.

TL;DR

• Distinguishing quantum hype vs progress using the Landscape of Quantum Computing and IBM Quantum Q1 2026 vs. Q4 2026

• Coinbase outlines PQ migration position

• Managing PQC migration, including testing CBOMKit to identify the cryptographic schemes a GitHub repo uses

• Solana explores FALCON signatures

There was definitely other news, such as the Q-Day Prize controversy or the Cisco Quantum Switch, but I’ll save it for the next one until I’ve fully researched it!

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Critical quantum: Skill of the Week

One of the most pertinent skills in quantum computing (and, frankly, in all of deep tech) is distinguishing hype from actual progress. Using critical graphs and quarterly reports from last week, I’ll explain how to read quantum content more critically.

Sam Jaques’ Landscape in Quantum Computing

Sam Jaques, a professor at the University of Waterloo, released his 2026 version of the Landscape in Quantum Computing graphs, which shows how far currently available quantum hardware is from a useful quantum computer.

The gray area shows the current available quantum hardware (with company-specific distinguishing points), based on the current number of qubits (the fundamental unit of a quantum computer) and error rates. Quantum computers are not practical for use until this gray area reaches the green area.

Comparing the 2026 graph to the 2021 version could lead to several misconceptions that have circulated.

Truth: Quantum computers have certainly grown by more than 400% (in terms of qubit count and error rate reduction) in the last five years.

Misconception: However, growth isn’t uniform, and we cannot assume that another 400% improvement will occur within 5 more years. We can’t assume that the error rate will be zero and that the number of qubits will be 10^3.199.

Quarterly Reports

Quantum computing benchmarking is very new and hasn’t fully developed industry standards, though tools such as the Quantum Benchmark Zoo do.

Although most Q1 quarterly earnings reports are released in May, developer ecosystem reports, such as the What’s New at IBM Quantum - Q1 2026, have already been released.

Many ecosystem reports include certain industry-wide benchmarks and omit others, company-specific benchmarks that may be inflated, lack comparisons to the previous quarter, or simply need more context, hindering effective evaluation of progress.

Though I wouldn’t consider IBM nefarious, let’s review their Q1 2026 statistics, contextualize and analyze what they indicate, and compare them with their Q4 2025 figures.

Q1 2026 Data:

Q4 2025 Data:

IBM uses two industry-wide benchmarks, both of which they originally created.

• Error Per Layered Gate (EPLG) is now an industry-standard metric, originally developed by IBM in 2023, that measures the probability that a single layer of a quantum circuit introduced an error.

  • More specifically, EPLG on an IBM QPU instance, also known as 2Q error layered, is defined as the average of the two-qubit error rate per layered gate for a 100-qubit chain. In other words, it’s the probability that a layer of two qubits fails.

  • The measurement is intended to assess the fidelity, the accuracy, and the reliability of a qubit or quantum operation.

• The best EPLG on the quarter report is the lowest EPLG among the 10 quantum processing unit instances that IBM Quantum runs. The instance with the lowest EPLG rate is the Heron r3 QPU in Boston, which improved by 0.04 percent, from 0.23 percent to 0.19 percent, since Q4 2025.

• Circuit Layer Operations Per Second (CLOPS) is now an industry-standard metric, developed by IBM in 2021, that measures the speed at which a processor can execute layers of a circuit.

  • The measurement is intended to assess how fast a quantum processor can process circuits.

• The best CLOPS on the quarter report is the highest CLOPS among the 10 quantum processing unit instances that IBM Quantum runs. In Q4 2025 and Q1 2026, the highest CLOPS was 330,000. Currently, the highest CLOPS are in Boston and Kingston (New York), at 340,000, so expect a higher CLOPS stat in the Q2 2026 report.

• The total available qubits, the number of fundamental units of a quantum computer available to users, decreased from last year, from 2344 to 2477 qubits.

  • This is due to the deprecation of IBM Brisbane, which had 127 logical qubits and many more physical qubits.

  • I noticed that this “qubit” count likely includes both logical qubits, which handle computation, and physical qubits that protect them, since the total number of logical qubits across 10 instances is 1430.

• The total number of academic papers that cite IBM Quantum and Qiskit has increased. It’s not a critical metric, as the substance of research matters more.

Publication of the Week

Coinbase’s position paper is a strong primer on quantum computing and its impact on blockchain and cryptography. It covers many of the points that I’ve highlighted in the last couple of weeks.

For those who are not new to this newsletter and want unique insights, I suggest:

4.3: Strategies and Security for Post-Quantum Signing (Page 30), which describes the risk and effort required to implement each type of strategy.

For example, the Move to 2-out-of-2 strategy requires a blockchain transaction to include both a post-quantum signature and a standard ECDSA/EdDSA signature.

• Yes to P1 (current security) as it does not compromise the current security standards.

• Yes to P2a (PQ security) as it implements post-quantum security.

• No, to P3 (cost now) as it does add significant cost to the current system.

• Maybe to P4 (change), as it is unclear how much it changes to the user flow and the current way of working.

4.6: The Cost of PQC at the Execution Layer (Page 37), which outlines how much more financially costly post-quantum cryptography is:

At 144 blocks per day, this implies storing about 86 MB of signature data per day, or roughly 31 GB per year, in signatures alone. Replacing these with PQ signatures—for example, ML-DSA with a 2,420-byte signature—would increase the block size by roughly 38x for the same number of transactions, yielding blocks of approximately 38 MB. At the same rate, this would require storing over 1 TB of signature data per year.

Presentation of the Week

JP Aumasson, Co-Founder and Chief Security Officer at Taurus SA, a digital asset infrastructure platform for institutions, published one of the more practical presentations on post-quantum cryptography.

My favorite slides and the ones I found most insightful were:

• Slide 7: This explains well what quantum computers are useful for.

• Slides 11-13: Provides a full overview of the digital areas (both blockchain and non-blockchain) that use RSA and elliptic cryptography:

What sets JP’s presentation apart from others I’ve seen is that he specifically groups the practical areas in real software systems that use cryptography and how to identify them (Slides 40-41):

He also outlines how to detect ongoing or planned PQ migrations and points to tools that make this visible.

I tested CBOMKit, an IBM-developed tool that scans an inputted open-source repository and produces a Cryptographic Bill of Materials (CBOM) listing cryptographic assets (such as algorithms, keys, certificates, and protocols), to test Apache Airflow, a popular open-source platform for managing batch workflows widely used in data pipelines.

CBOMKit found that 19.2% of the cryptographic algorithms used by Apache Airflow are not quantum-safe.

The cryptographic algorithms authenticate to workloads and ensure that no unauthorized parties can execute or interact with scheduled tasks. Updates will be complex, as 12 types of cryptographic assets were found, spanning 7 primitives (algorithm types) and 3 functions (use cases).

If I were using Apache Airflow regularly, I would ask the Apache Foundation about their PQC roadmap, as JP would have recommended.

Here’s a screen recording of the final result by CBOMKit:

Note: If you plan to use CBOMKit to analyze open-source GitHub repositories to determine whether they are quantum-safe, make sure to increase your Docker Resource allocation, as most significant repos will hit a memory limit. DM me if you need help!

Other News

• Firedancer and Anza, two validator clients (software for running blockchain nodes) on Solana, implemented a prototype of FALCON signature verification on their validator clients.

  • They chose FALCON because its verification time is comparable to the current one, despite its large signature sizes. Solana does not need to prioritize a smaller signature size as much as Ethereum, since it has much fewer validators (Ethereum has 905,000 vs. Solana's 767) and does not need to store as many. They want to prioritize matching the same transaction speed.

  • An Anza article states, “None of this constitutes a commitment to a specific post-quantum signature scheme.” If Solana isn’t ready to commit to FALCON, this could mean:

    • Solana wanted to compete with Ethereum, which has been leading the way in publicly announcing research initiatives in post-quantum cryptography.

    • But I would ask: If Solana isn’t committing to FALCON, what’s the alternative for them? What else is in the research pipeline?

  

• Anza also implemented a prototype mechanism that would allow a user to bind a post-quantum key to an existing key.

  • A core challenge is that once a migration is complete, blockchain users must migrate their existing keys (think of them as a bank account number and password) to post-quantum ones to continue using and accessing the blockchain.

    • I previously mentioned that much of the risk arises from users migrating incorrectly or being phished during the process.

    • Another interesting challenge Anza states that I haven’t thought of deeply is that changing keys effectively changes the identifier others use to send funds. This means users would need to update every app and every person they send or receive crypto to or from.

  • One interesting approach is to allow a user to create a zero-knowledge proof that the user “owns” the existing account and authorizes binding a new post-quantum public key to it, preserving the original address.

This week’s roundup is too long for email, so please check it out on the Substack app.

TL;DR

• Solutions: BIP-361 Bitcoin proposal, Quantum-Safe Bitcoin, Taproot wallet post-quantum recovery

• Industry Moves: More blockchains announce PQ migration; Meta releases internal PQ prioritization chart

• Technical: PQ Crypto Registry for benchmarking algorithms

• Breakthroughs: NVIDIA’s Ising AI models for quantum computer calibration tasks

• Educational Resources: Fancy Cryptography, IBM Quantum Computing 101 poster, Miden PQ signatures poster

And Happy Quantum Day to anyone who celebrated on April 14th!

📘 Definition of the Week

Fancy cryptography consists of cryptographic schemes that are based on unique mathematical algorithms or approaches, or that use standard primitives in unusual ways.

If you are working on fancy cryptography, I suggest that you include your work in this GitHub repository.

An example is the password manager 1Password, which uses the Secure Remote Password method to allow users to authenticate with its servers without the server needing to know the password or transmit it.

🎨 Graphics of the Week

IBM’s simple Quantum Computing 101 poster that explains quantum computing in under a minute.

Audience: Ideal for those without any foundational knowledge of quantum computing

Miden’s Post-Quantum Signatures Benefits and Trade-Offs poster that explains why today’s encryption is not quantum-resistant and the current post-quantum signature types under discussion.

Like last post-quantum roundup, I’m grateful that Miden continues to highlight other post-quantum signature families, rather than blindly accepting the most popular ones.

Audience: Ideal for those who are familiar with quantum threats and need a quick overview of post-quantum cryptography options

Meta’s newly released post-quantum cryptography migration prioritization chart, which they are using internally to assess systems

Meta did not specify which of their systems fell into which priority categories, but if I were to take an educated guess, a few top priorities to migrate to post-quantum cryptography would be:

• Direct messages on WhatsApp are currently encrypted using public-key cryptography, so only you and the person you’re communicating with can view them.

• Login systems to Instagram, Facebook, WhatsApp, etc.

Audience: Ideal for technical leads and C-Suite tech executives who are mapping out their companies’ post-quantum migration strategies

📚 Resource of the Week

PQ Crypto Registry benchmarks post-quantum cryptographic algorithms for practical use. Similar resources include the PQ Signature Zoo and Open Quantum Safe.

Using ML-DSA, or Module-Lattice-Based Digital Signature Algorithm, and formerly known as CRYSTALS-Dilithium, as an example, here’s how one would read the registry.

First, ML-DSA is a digital signature scheme that generates a digital fingerprint, or the digital equivalent of a physical signature, used for identity verification.

Security

It is secured by three approaches: Module-LWE & Module-SIS, and SUF-CMA.

Module-LWE and Module-SIS are based on lattices, infinite sets of regularly spaced points in space, and are more complex to solve than elliptic curves, on which Elliptic Curve Cryptography, a non-quantum-resistant form of cryptography, is based. Module-LWE (Module Learning With Errors) is a mathematical problem where the adversary must distinguish a noisy lattice structure from completely random data. Module-SIS (Module Short Integer Solution) is a mathematical problem where, given a matrix that defines a lattice, the goal is to find a short nonzero vector in a specific lattice.

If you are inclined to go deeper into the mathematics, I suggest YouTube videos by Professor Alfred Menezes of Waterloo, such as this one, and his lecture notes.

ML-DSA is also secured by SUF-CMA (Strong Existential Unforgeability under Chosen-Message Attack), which guarantees that an attacker who accesses a specific signature cannot use it to generate any new valid signature for a specific or another message.

Standard

ML-DSA is standardized by the U.S. National Institute of Standards and Technology for adoption and use by federal departments and agencies, and its standard is published as FIPS 204.

Parameters, Levels, PK, SK, and Sig

Major determining factors for adopting ML-DSA include its security levels and key and signature sizes.

ML-DSA has three parameter sets (ML-DSA-44, ML-DSA-65, ML-DSA-87), each associated with predefined constants in its algebra that provide security guarantees. I was initially going to call them “versions” of ML-DSA (which is more intuitive), but I would probably get in trouble with some cryptographers if I did.

For ML-DSA, the higher the number associated with the parameter set, the stronger the predefined constraints and the more secure it is. For example, the collision strength, or the property that makes it extremely hard to find two inputs that produce the same internal value when signing, is highest for ML-DSA-87 (value: 256 bits), higher than for ML-DSA-65 (value: 192 bits), and even higher than for ML-DSA-44 (value: 128 bits).

ML-DSA-87 is more secure than ML-DSA-65, and ML-DSA-65 is more secure than ML-DSA-44.

The resource lists the NIST security level (on a scale of 1-5, with 5 being the highest) for each “version.” ML-DSA-44 is Level 2, resistant to attacks like collision finding in SHA-256 (2^128 operations). ML-DSA-65 is Level 3, resistant to breaking AES-192 (2^192 operations). ML-DSA-65 is Level 5, the highest level, resistant to breaking AES-256 (2^256 operations).

The more secure the version, the larger the sizes (in bytes) of its public key (PK), private key (SK), and signature (Sig). Systems that want stronger security against quantum-initiated attacks must trade off increased data storage, higher latency, and longer signature verification times.

The resource provides an overview of the risks associated with each cryptographic scheme:

• Assumption: the “security” strength of the underlying mathematical problems on which the scheme relies

• Implementation: the risk introduced when integrating and correctly implementing the scheme in software

• Side-channel: the risk of sensitive information leaking through physical or observable behavior during execution

In the case of ML-DSA, the assumption is low, implementation (difficulty) is high, and side-channel (risk) is medium.

📚 Discussion of the Week

This week, the Bitcoin community introduced various approaches to post-quantum migration, prompting a range of opinions.

From previous roundups, I’ve often mentioned how the Ethereum community has spearheaded post-quantum migration conversations in the blockchain community, but now more blockchains are following suit with bold timelines: Bitcoin, TRON, StarkNet, Sui, and Arc. However, production-grade implementations have not been made.

H.E. Justin Sun, founder of TRON, says that TRON will be the first major blockchain to deploy post-quantum cryptographic signatures on its mainnet, its production version.

Kostas Kryptos, Co-Founder of Mysten Labs and a major contributor to Sui, claims that his personal keys will be migrated to post-quantum keys within the next 30 days.

We’ll see which implementations prevail over the coming weeks and months. The blockchain community has a bad reputation, not for delivery but for overstated marketing, and technical questions often go unanswered:

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So, what’s up with Bitcoin?

The most controversial proposal is BIP-361: Post-Quantum Migration and Legacy Signature Sunset. It does not propose a specific cryptographic scheme; instead, it focuses on freezing users' Bitcoin assets if they do not migrate to a future post-quantum cryptographic scheme.

In Phase A, users will not be allowed to send Bitcoin to any keys generated by a non-quantum-resistant cryptographic scheme. In Phase B, users cannot make any transactions using a key that uses non-quantum-resistant signatures.

This worries many Bitcoin traders and influencers, as it sets a precedent for freezing Bitcoin assets in other situations, which runs counter to Bitcoin’s original values.

Another proposal that generated attention but was less controversial was quantum-safe Bitcoin transactions without a soft fork or needing to change the Bitcoin protocol itself, introduced by Avihu Levy, Chief Product Officer at StarkWare.

In addition to the main GitHub, you can check out this livestream of Avihu explaining the paper:

Here’s a graphic explaining the concept by Akash Balasubramani, Ecosystem Manager at StarkWare:

In a nutshell, instead of upgrading the signature scheme used in Bitcoin, this approach changes what the wallet actually does when you try to send funds. Instead of producing a signature instantly using a private key when sending a transaction, the wallet repeatedly tries random values and hashes them until it finds one that Bitcoin accepts as a valid signature under its existing rules. Another way to think of it is that the wallet runs a small computational search in the background before it can construct the transaction. Once a valid result is found, the transaction is assembled and broadcast just like any other Bitcoin transaction.

The key idea is that the security no longer comes from the traditional signing process, but from the difficulty of finding such a valid value in the first place.

However, in this proposal, transactions become expensive and slow to generate, making this impractical for everyday or mainstream use. It also doesn’t prevent a quantum computer from iterating through all possible ECDSA private keys until it finds one that matches the keys, so, in the long term, Bitcoin still needs to use a post-quantum cryptographic scheme.

Related to discussions around “freezing” assets in a post-quantum scenario, an idea is a recovery path for keyspend-only Taproot wallets. Users can use Bitcoin in keyspend-only taproot wallets solely by signing with a Schnorr signature, which is not quantum-resistant.

If Bitcoin were to disable Schnorr signatures in an emergency, removing this method of authorizing transactions right away, these wallets could become stranded with no valid way to move funds. A proposed solution uses a zero-knowledge proof to prove that a Taproot output key was derived from a BIP-32 wallet seed and derivation path, without revealing the seed or the master password, allowing the rightful owner to move funds to a post-quantum-secure address.

There are now a plethora of proposals; other post-quantum proposals for Bitcoin can be tracked here.

Other Highlights

• Using AI to improve quantum computers is becoming a reality. NVIDIA released Ising, AI models focused on identifying and correcting errors on quantum computers.

  • It benchmarked its models against other popular ones, such as (Google) Gemini-3.1-Pro, (Anthropic) Claude Opus 4.6, and (OpenAI) GPT-5.4, and found that it was at least 2% and as much as 10% effective at tasks involving calibration, or tuning parameters to make qubits behave correctly. It outperformed the models on five of the six tasks.

    

  • Will the quantum computing industry adopt mainstream models (Gemini, Opus, and GPT), rely more on domain-specific models (Ising), or both? Is it too early to tell? Vote below to let me know you think!

Opportunities

• The 2026 Quantum Computing User Forum, hosted at Oak Ridge National Laboratory from July 20 to July 24, is for quantum computing users to discuss common practices for developing applications, software, and simulations for quantum computing devices and systems. Register by May 15, 2026.

• WISER Quantum and AI Program 2026 is a free, six-week virtual summer program for students and previous hackathon winners on classical algorithms, quantum computing, and artificial intelligence. Apply ASAP (program starts June 24th).

  Thanks for reading Realmscape: Quantum & Cryptography! This post is public so feel free to share it.

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My main motivation for writing this article is to help readers understand how to interpret quantum computing papers, especially as the field becomes more mainstream and sensational claims spread widely.

In a new white paper, researchers at Google Quantum AI, Stanford, and the Ethereum Foundation developed much smaller and less resource-intensive quantum circuits, or programs that run on a quantum computer, capable of breaking Elliptic Curve Cryptography (ECC).

It’s significant because it is now estimated that less time on a less powerful quantum computer will eventually be needed to break ECC, a widely used cryptographic scheme that secures much of the Internet and digital protocols.

It’s also noteworthy that, instead of publicly releasing the quantum circuit, the team used zero-knowledge proofs to verify the circuits without disclosing their contents.

Zero-knowledge proofs (zk proofs) are cryptographic methods by which one party can prove to another that something is true, without revealing any information.

So how do we verify that these quantum circuits exist?

This article explains the circuits and focuses on answering this exact question: how to independently verify these zk proofs and confirm that these “private” quantum circuits exist.

Why use zero-knowledge proofs

Industry leaders highlight the growing use of zk proofs to conceal important quantum circuits, emphasizing the need to understand and verify them.

It suggests an emerging trend that researchers want to commercialize circuits, or keep them away from, or face government pressure to withhold them from bad actors.

The white paper states they are not releasing circuits publicly, unlike previous researchers, as bad actors could use them once practical quantum computers are available:

Justin Drake, co-author of the white paper and researcher at the Ethereum Foundation, suggested that more valuable, important circuits will remain unpublished:

Nic Carter, a major Bitcoin investor and co-founder of Castle Island Ventures, compares the use of a zk proof to the classification of nuclear research, as the atomic bomb was developed:

It becomes critical to understand how to verify them, as more researchers adopt zk proofs to hide, yet “prove” specific quantum circuits exist.

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What Google’s quantum circuits mean

Google Quantum AI researchers provided the metadata for two quantum circuits capable of breaking ECC.

A circuit is considered capable of breaking ECC if it can solve 9,024 elliptic curve point addition problems with different starting point inputs.

Given two starting points on an elliptic curve, Points P and Q, the circuit can find the third point, Point (-R), where the line passes through P and Q intersects with the curve. Then, it computes Point R by reflecting Point (-R) across the x-axis. R is reflected as the sum, or addition, of P and Q.

In more mathematically direct terms:

correctly computes point addition on the elliptic curve secp256k1 [the type of elliptic curve used in Bitcoin] across all 9,024 pseudo-random inputs deterministically derived from the circuit’s own hash

Most elliptic curves are less uniform than this example, and it is not obvious to an everyday, classical computer where the third point lies, which makes ECC traditionally very secure for encrypting digital data, as explained in this video:

Therefore, solving 9,024 of these problems is no easy task. Quantum circuits that can solve 9,024 instances, as the researchers at Google Quantum AI claimed, show it can reliably perform the elliptic curve arithmetic required for a full ECC attack.

Google Quantum AI presented detailed information on two circuits that satisfied this criterion; each circuit was optimized for distinct objectives.

1. The first approach uses fewer qubits, or quantum computing units, making it more optimized for hardware limitations.

2. The second uses fewer gates or computing operations, making it more optimized for runtime performance.

Having two circuits optimized for different objectives allows them to be run on various types of quantum computers better suited to specific tasks, such as hardware or performance.

Circuit metadata

Although these quantum circuits require as few as 70–80 percent fewer resources than other circuits capable of breaking ECC, they are still too large to run as programs on a quantum computer. Their performance remains based on theoretical assumptions, although they should not be ignored.

The circuit metadata included the number of non-Clifford gates, which are operations required for universal quantum computation, and the number of logical qubits, which are qubits that carry out computation while being protected from noise and errors by many surrounding physical qubits.

The quantum circuit with fewer qubits, or the “low-qubit quantum circuit,” included:

• 2,700,000 non-Clifford gates

• 1,175 logical qubits

The quantum circuit with fewer gates, or the “low-gate quantum circuit,” included:

• 2,100,000 non-Clifford gates

• 1,425 logical qubits

Verifying the metadata

How the zero-knowledge proof was created

A zero-knowledge proof was generated for each quantum circuit, yielding three assigned identifiers for verifying its metadata.

Here are identifiers for the low-qubit quantum circuit presented in the white paper:

Circuit SHA-256 Hash:
0xcc8f532ffea1583ceed3c9af75de3263ebaddd5fdf3cddfb3dea848b94d0396a

Verification Key:
0x00ca4af6cb15dbd83ec3eaab3a0664023828d90a98e650d2d340712f5f3eb0d4

Groth16 Proof Bytes:
0x0e78f4db0000000000000000000000000000000000000000000000000000000000000000008cd56e10c2fe24795cff1e1d1f40d3a
324528d315674da45d26afb376e86700000000000000000000000000000000000000000000000000000000000000000215c7fe4fc59
7b861d82370ab556684ae36e98cf073e7f754f2788ad58721dbd012927516f316e7b4f3effb1dbd567732611cb0334f2d75e529c5e3
becd0629c17605c7ff87c6f23324328744454bdec0df425a4a63e3358c10079c85ef757412ae86ae1f85bf47ef6980852d6f65423be
2d90adb5b29896493324128b1cda0a0042f7138c850a1ca441210ba770a2eee39d56f6f90bf68b7a346e1658c6529715334621b6e1a
63b85875b8c8a610e0d885662879755803027dad57d97140afb2498bbb63215b236575f95b0019f2b9713bc810e1e044d47ab360e92
b899c46512fc97460609186bf1fe01c892a8015fb00e7fdea11b08f88c6adb79b1243518

And the identifiers for the low-gate quantum circuit:

Circuit SHA-256 Hash:
0x24f5758f2216aa87aa2806af32a0db788767b873cf6869510cca3d893b3f8a69

Groth16 Proof (Hex):
0x0e78f4db0000000000000000000000000000000000000000000000000000000000000000008cd56e10c2fe24795cff1e1d1f40d3a
324528d315674da45d26afb376e867000000000000000000000000000000000000000000000000000000000000000000a11fe07d3af
e9d5e9b5af9fdb37fc38bd529d09b92e08350556a3a38ad03f1b2ed337741ecfeae1a65849d1927cdfc3ea4d211734cd747fc4a5534
449ebfd1e2130fde87661e0e0fba6ec2055c130d875c7fa3358e25e2236e928520eddfa992a9e6510d0635161c62e0e29f4c28921f5
6126a908b286c4d910089780441a5811799d5c7dbf293ac3e6d5f51267efbf95cf8643cb28c5f7c2bac8ee9d4b55c830475b328ff9f
9b257f2383e7934aaab12616e04645bf6a2b9820cafba4fd3830655d676b7ff376817bbd18a178cf091ad4f4e53b2e322a1d75b3e14
00d9b66e1feb401eae0df274d7a774f0bd2fc471ce574348daeaac3ee288dcd282456a33

Verification Key:
0x00ca4af6cb15dbd83ec3eaab3a0664023828d90a98e650d2d340712f5f3eb0d4

Circuit SHA-256 Hash

First, researchers created a Circuit SHA-256 Hash for each circuit.

The KMX file containing the quantum circuit code was converted to a “hash,” or unique 66-character string, using the SHA-256 function. SHA-256 hashes cannot be easily reversed to reveal the original text.

Groth16 Proof Bytes and Verification Key

Then, researchers created an ELF binary, a list of rules that a zero-knowledge proof needed to “prove” or validate.

The ELF binary is a RISC-V program written in assembly language or C/C++, and the code must reflect an example statement such as this that proves the quantum circuit exists:

Zero Knowledge Proof Statement 1 (Low-Qubit Variant)

We possess a quantum kickmix circuit C low-qubit (uniquely committed to via its cryptographic hash) with resource counts of at most:

2,700,000 non-Clifford gates (CCX + CCZ)

1,175 logical qubits

17,000,000 total operations

that correctly computes point addition on the elliptic curve secp256k1 across all 9,024 pseudo-random inputs deterministically derived from the circuit’s own hash.

This introduces a significant trust assumption. Readers must trust that researchers created an honest and accurate ELF binary, since the circuits are hidden. Independent audits of ELF binaries are critical, but none have been conducted yet (though I’ve considered doing one myself; tools such as Ghidra can be used to evaluate ELF binaries).

Then, researchers used the ELF binary and the circuit to verify that the circuit met all the rules specified in the ELF binary.

Researchers would run the ELF binary with the circuit as its input inside a SP1 zero-knowledge virtual machine (zkVM), a sandboxed computing environment developed by Succinct Labs that executes instructions (such as those in an ELF binary), verifies computations, and produces zero-knowledge cryptographic proofs upon verification.

In this case, first, the zkEVM processed the ELF binary and hashed it to create a verification key.

Then, the zkVM followed the ELF binary instructions to check that the circuit correctly computed elliptic curve point addition across all 9,024 test inputs.

Upon verification, the zkEVM generated a STARK proof, a (yes, post-quantum secure) cryptographic string confirming verification and cross-checkable with the verification key and ELF binary.

An original STARK proof is relatively large and slower to verify, so it was compressed into Groth16 Proof Bytes, a version of a SNARK (another class of zero-knowledge proofs) that is smaller and cheaper to verify.

Anyone can use the Groth16 Proof Bytes together with the verification key in Step 2 to verify the result in milliseconds without the original circuit, re-computation, or trusting researchers.

How to independently verify the proof

The easiest way to verify the proof is to use the provided identifiers and the verification program in the public Zenodo archive, a general-purpose open repository for research and data that is usable on any typical computer. I ran the upcoming terminal commands on my Mac laptop.

Verifying the proof confirms that quantum circuits exist that satisfy the requirements defined in the ELF binary. These requirements were to solve 9,024 elliptic curve addition problems within the resource limits specified for the low-qubit and low-gate quantum circuits described in the Google Quantum AI white paper.

It does not confirm that the quantum circuits were successfully executed on a quantum computer (which they were not) or that the ELF binary had the correct verification logic and properly checked the quantum circuits.

Step 1: Download zkp_ecc_zenodo.zip from the provided Zenodo archive and extract it.

The directory structure should contain:

zkp_ecc_zenodo/
├── verifier/
│   ├── verifier.rs       ← the verification program
│   └── Cargo.toml        ← its dependencies
├── proofs/
│   ├── zkp_ecc-program   ← the ELF binary
│   ├── vkey.bin          ← the verification key
│   ├── low_qubits/
│   │   └── proof_9024.bin  ← proof for the low-qubit circuit
│   └── low_toffoli/
│       └── proof_9024.bin  ← proof for the low-gate circuit
└── run_proofs.sh         ← script for regenerating proofs (requires GPUs)

The five most important files are:

• proofs/zkp_ecc-program: the ELF binary

• proofs/vkey.bin: the verification key

• proofs/low_qubits/proof_9024.bin: Groth16 Proof Bytes for the low-qubit circuit

• proofs/low_toffoli/proof_9024.bin: Groth16 Proof Bytes for the low-gate circuit

• verifier.rs: the verification program, which will be explained further in the following sections

Step 2: Install the dependencies

The verifier is written in Rust and depends on the SP1 SDK, which depends on protobus for its data serialization format.

brew install protobuf

Step 3: Review the verifier.rs, the verification program

The verification program, found at verifier/verifier.rs, confirms that the zk proof corresponds to a valid execution of the verification logic.

In other words, it verifies that the circuit was evaluated according to the ELF binary and satisfied the claimed specifications of the quantum circuits, as explained in the “How the zero-knowledge proof was created” section.

It does this by checking the Groth16 Proof Bytes against the verification key, which is the compressed representation of the ELF binary constraints.

First, it reads the verification key:

let vk_bytes = std::fs::read(&vkey_path).expect("failed to read vkey file");

Then, it loads the Groth16 Proof Bytes:

let mut proof = SP1ProofWithPublicValues::load(&args.proof).expect("failed to load proof");

It uses the SP1 SDK to verify the proof against the verification key.

client.verify(&proof, &vk, None).expect("failed to verify proof");

If the verification succeeds, it returns an output as shown in Step 5.

Step 4: Run the verifier

Once the verification logic is understood, the program can be executed to check the proof.

The verification program requires two inputs: Groth16 Proof Bytes and the verification key of a specific circuit.

Low-qubit circuit

In the case of the low-qubit circuit, the Groth16 Proof Bytes are stored in proofs/low_qubits/proof_9024.bin. Run the verifier within the zkp_ecc_zenodo folder for the low-qubit circuit with this command:

RUST_LOG=info cargo run --release -p verifier -- \
    --proof proofs/low_qubits/proof_9024.bin \
    --vkey proofs/vkey.bin

Low-gate circuit

In the case of the low-qubit circuit, the Groth16 Proof Bytes are stored in proofs/low_toffoli/proof_9024.bin. Run the verifier within the zkp_ecc_zenodo folder for the low-qubit circuit with this command:

RUST_LOG=info cargo run --release -p verifier -- \
    --proof proofs/low_toffoli/proof_9024.bin \
    --vkey proofs/vkey.bin

Step 5: Review the output

If the verification succeeds, the verification program confirms that the zk proof corresponds to the valid execution of the verification logic and returns an output.

The output should match the provided metadata for each circuit.

✅ Low-qubit circuit:

• Circuit SHA-256 Hash / Circuit hash commitment:
  0xcc8f532ffea1583ceed3c9af75de3263ebaddd5fdf3cddfb3dea848b94d0396a

• Verification Key / Verifying Key (Hex)):
  0x00ca4af6cb15dbd83ec3eaab3a0664023828d90a98e650d2d340712f5f3eb0d4

• Non-Clifford gates / Demanded Average non-Clifford count: 2,700,000

• Logical qubit count / Demanded Qubit count: 1,175 logical qubits

Output:

Verifying Key (Hex): 0x00ca4af6cb15dbd83ec3eaab3a0664023828d90a98e650d2d340712f5f3eb0d4
Proof (Hex): 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
Successfully verified Groth16 SNARK proof.
Circuit hash commitment: 0xcc8f532ffea1583ceed3c9af75de3263ebaddd5fdf3cddfb3dea848b94d0396a
Demanded Number of tests: 9024
Demanded Qubit count: 1175
Demanded Average non-Clifford count: 2700000
Demanded Total ops: 17000000

✅ Low-gate circuit:

• Circuit SHA-256 Hash / Circuit hash commitment:
  0x24f5758f2216aa87aa2806af32a0db788767b873cf6869510cca3d893b3f8a69

• Verification Key / Verifying Key (Hex):
  0x00ca4af6cb15dbd83ec3eaab3a0664023828d90a98e650d2d340712f5f3eb0d4

• Non-Clifford gates / Demanded Average non-Clifford count: 2,100,000

• Logical qubit count / Demanded Qubit count: 1,425 logical qubits

Output:

Verifying Key (Hex): 0x00ca4af6cb15dbd83ec3eaab3a0664023828d90a98e650d2d340712f5f3eb0d4
Proof (Hex): 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
Successfully verified Groth16 SNARK proof.
Circuit hash commitment: 0x24f5758f2216aa87aa2806af32a0db788767b873cf6869510cca3d893b3f8a69
Demanded Number of tests: 9024
Demanded Qubit count: 1425
Demanded Average non-Clifford count: 2100000
Demanded Total ops: 17000000

Conclusion

Google Quantum AI researchers developed quantum circuits capable of breaking ECC that are not publicly released, but are verifiable using zero-knowledge proofs.

Researchers may increasingly rely on zk proofs to commercialize circuits, prevent misuse, or respond to government pressure while still publicly demonstrating that they have made a breakthrough.

Running the verifier confirms that quantum circuits exist that satisfy the statements committed to in the proof. However, it does not confirm that the quantum circuits were ever successfully run on a quantum computer or that the ELF binary itself contains the correct verification logic.

As more researchers use zero-knowledge proofs to support claims about undisclosed quantum circuits, independent verification and audits of proofs will become increasingly important.

This week’s roundup is too long for email, so please check it out on the Substack app.

TL;DR

• Solutions/Demos: Post-quantum Ethereum wallet testnet, SHRIMPS reduces Bitcoin PQ signatures

• Academic Research: Quantum threat to ECC sooner

• Breakthroughs: Hybrid quantum-classical protein simulation

• Technical: Benchmarking alternative PQ signatures

• Quantum events and opportunities: NVIDIA Quantum Day, Google’s Willow QPU access, Vanderbilt Quantum Forum

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📘 New post-quantum solutions and demos

Daisugi, EVM-compatible testnet to test post-quantum wallets

Daisugi is a new EVM-compatible testnet (a testing environment compatible with Ethereum) with a website where you can create a (currently free) wallet that uses a post-quantum signature scheme.

Try it out 👉 daisugi.fyi

Main value-add: It demonstrates how using post-quantum wallets is similar to today’s Elliptic Curve Cryptography-based wallets, but the costs of use and speed vary significantly.

On the website, you can select from two types of FALCON or Dilithium signature schemes to create a wallet based on your preferences.

The process was quite straightforward. I was easily able to create a wallet that uses FALCON-512 Direct, as shown in this video:

And then created a wallet using Dilithium-2 Direct, which had the same exact process and similar creation time:

The experience of sending test ETH to different wallets was the same as today, but the costs were much higher:

A typical transaction on Ethereum usually requires 21,000 units of gas or 0.0045 USD at the time of writing this article.

• 21,000 as the units of gas

• 0.104 as the base price for gas

• 0.000000001 as the conversion back to ETH

Sending 0.1 test ETH from the wallet that uses FALCON-512 Direct signatures to any other wallet used 81,968, or 0.000008524672 ETH, or 0.017 USD, 3.9 times more than the current ECDSA.

Sending 0.1 test ETH from the wallet that uses Dilithrium-2 Direct signatures costs 120,270 units of gas, or 0.00001250808 ETH, or 0.026 USD, which is 5.7 times more than the current ECDSA and 1.47 times more than FALCON-512.

SHRIMPS, a smaller-sized post-quantum signature scheme (for Bitcoin)

SHRIMPS is a new hash-based signature proposal designed specifically for Bitcoin, with a first signature size of 2.5 KB at 128-bit quantum security, while subsequent signatures are standard, post-quantum SPHINCS+ signatures (7.8 KB).

Though SHRIMPS is still much larger than ECDSA signatures (0.064 KB), the progress towards more compact signature sizes makes post-quantum signature schemes more practical.

Read the full post 👉 delvingbitcoin.org

How it works:

The same Bitcoin public key can be loaded on up to 1,024 independent backup devices.

Two SPHINCS+ signature instances are available under a single public key:

1. a compact path used the first time a device signs (2.5 KB signature size)

2. a larger fallback path for any subsequent signatures (7.8 KB signature size)

When the device loads the public key, and a signature is requested, if the public key has not been signed on that device before, it will use the compact path signature. If the public key has already been signed, it will use the fallback path signature.

Main value-add: Significantly reducing the PQ signature size of the first signature a device signs with a public key remains valuable, even if subsequent signatures are larger. Bitcoin keys are rarely used more than a few times, so in practice, many signatures are on the compact path.

Academic papers of the week

The quantum computing community has been buzzing this week over the release of two papers by acclaimed academics on the earlier countdown and the fewer qubits needed to break widely used Elliptic Curve Cryptography (ECC).

The main value of these papers is that they show how improved qubits and methods are enhancing the capabilities of quantum computers.

The conversation has been so widespread that including it here felt repetitive, but it’s encouraging to see many well-known, non-academic voices in the crypto space discussing it.

From , a major Bitcoin investor:

Haseeb Qureshi, Managing Partner of Dragonfly, a leading crypto fund:

Charles Guillemet, CTO of Ledger, the most popular crypto hardware wallet:

Though an academic, even Professor Scott Aaronson, one of the most well-known professors in quantum computing, chimed in with:

Babbush, R., Zalcman, A., Gidney, C., Broughton, M., Khattar, T., Neven, H., Bergamaschi, T., Drake, J., & Boneh, D. (2026, March 30). Securing elliptic curve cryptocurrencies against quantum vulnerabilities: Resource estimates and mitigations. Google Quantum AI. https://quantumai.google/static/site-assets/downloads/cryptocurrency-whitepaper.pdf

The blog version: https://research.google/blog/safeguarding-cryptocurrency-by-disclosing-quantum-vulnerabilities-responsibly/

A new whitepaper from Google Quantum AI, co-authored with researchers from Stanford, UC Berkeley, and the Ethereum Foundation, provides updated resource estimates for breaking ECC, which secures Bitcoin and Ethereum wallets today.

Using Shor’s algorithm, ECC could be broken with approximately 1,200 logical qubits and about 90 million quantum operations, requiring roughly 20 times fewer resources than earlier estimates, as shown in this graph comparing the paper’s work with previous research.

On a sufficiently optimized superconducting quantum computer, the attack could complete in about nine minutes, close to Bitcoin’s 10-minute average block time.

The paper emphasizes that blockchains need to protect against two types of attacks:

(Unofficially) The Definitions of the Week:

• At-rest attacks, which target wallets whose public keys are already exposed on-chain.

• On-spend attacks, where an attacker intercepts a transaction after it is broadcast but before it is confirmed.

If you are looking for a concise yet in-depth breakdown of this paper, I suggest reading this post from Justin Drake, one of the co-authors:

Cain, M., Xu, Q., King, R., Picard, L. R. B., Levine, H., Endres, M., Preskill, J., Huang, H.-Y., & Bluvstein, D. (2026). Shor’s algorithm is possible with as few as 10,000 reconfigurable atomic qubits (arXiv:2603.28627). arXiv. https://arxiv.org/abs/2603.28627

The blog version: https://www.oratomic.com/news/launch-announcement

A new paper from researchers at Caltech, Harvard, and MIT about a quantum computing company called Oratomic shows that Shor’s algorithm could operate at cryptographically relevant scales with just 10,000 highly specialized, “reconfigurable” neutral-atom qubits (qubits that use neutral atoms or trapped ions as their main tech) to break ECC. 26,000 qubits are needed if you want to do it within a few days.

The reduction comes from combining three improvements:

1. high-rate quantum error-correcting codes

2. more efficient logical instruction sets

3. optimized circuit design.

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Other highlights this week include:

💻 Breakthroughs

• IBM and the Cleveland Clinic combined quantum and classical computers to perform a hybrid technique, sample-based quantum diagonalization, for simulating this protein.

• • In sample-based quantum diagonalization, a quantum computer analyzes the data and identifies focus areas, and a classical computer refines the results and produces the final results.

• Researchers were able to simulate the same properties of the chemical compound KCuF₃ on an IBM Heron quantum processor (156 logical qubits, though the study used up to 50).

💻 Technical

• Privacy Ethereum organized a two-day, fully remote internal hackathon to explore the outcomes when a team of cryptography engineers focuses intensively on AI-assisted development.

  • A developer created a protocol to send “private,” anonymous transactions without traceability to the original wallet (like Tornado Cash) using post-quantum cryptography.

  • Main value-add: It’s the first time that I’ve seen “STARKs” implemented as the only post-quantum solution. STARKs, a type of zero-knowledge proof that verifies a computation was performed correctly without revealing the underlying data, and they are considered post-quantum secure because they rely entirely on hash functions rather than ECC.

• The Ethereum Community Conference this year was full of talks on post-quantum cryptography, but this was my favorite, as Alexander John Lee is the only crypto engineer I’ve found who has openly shared benchmarking on less conventional post-quantum digital signature schemes.

  • Main value-add: It is valuable to have engineers like him who evaluate multiple solutions rather than blindly choosing a recommended or popular solution.

    • Alexander John Lee (Miden), Andrey Ivasko (researcher) - Comparing & Benchmarking Post Quantum Digital Signature Schemes

• Some less popular post-quantum signature scheme types that they cover in the talk, and which I learned about thanks to the graphic below that Alexander John Lee shared recently:

  • Codes - rely on the difficulty of decoding a random linear error-correcting code. Require very large public keys.

  • Isogenies - rely on the difficulty of finding a secret isogeny, a special mathematical relationship that maps one elliptic curve to another while preserving its structure. Can produce small signatures, but are quite complex to implement.

  • Multivariate - rely on the difficulty of solving systems of polynomial equations. Can produce small signatures and are fast to verify, but key generation and key sizes can be large.

🚀 Opportunities

• Sign up to attend NVIDIA Quantum Day on April 14, 2025, a free virtual event from 8 A.M. to 1:30 P.M. PST that highlights the latest advancements in accelerated quantum computing development.

  • I’m most excited to hear about how AI is being used to advance quantum computing, and looking forward to this talk:

AI for Calibration: Automating Quantum Hardware - Discover how AI-driven calibration accelerates tuning of qubits and control systems, boosting stability, throughput, and hardware uptime.

• • It’s because, in a recent podcast with Brian Gaucher, a former engineer at IBM, he mentions that future quantum computing systems (i.e., 100,000 qubits) will become too large to manage manually. Instead of stopping algorithms for months, AI will help tune qubits to behave as expected.

• The Vanderbilt Quantum Forum in Nashville, Tennessee, on April 9, 2026, is a one-day, in-person conference focused on quantum technology, public policy, and economic impact. Government employees can purchase a discounted ticket for $35, while regular-priced tickets are $100.

• Google has opened applications for early access to its 105-logical-qubit Willow quantum processor. Apply by May 15, 2026.

P.S. I severely underestimated the scope of this week’s roundup, but rest assured that future ones will be released at 1 PM PST. Happy Thursday in PST still! If quantum computing and post-quantum cryptography moved as fast as they did this week, I might have to consider multiple “themed” editions during the week.

The Post-Quantum Roundup will now be released on Thursdays, Pacific Standard Time, based on subscriber feedback about a regular cadence. It also includes more editorial for more value than a simple newsletter with links.

This week’s roundup is too long for email, so please check it out on the Substack app.

📘 Definition(s) of the week

• Neutral atom quantum computers - quantum computers that use atoms without an electrical charge as qubits. Reference: Pasqal, a French quantum computing company founded by 2022 Nobel Prize in Physics winner Alain Aspect

• Qubit modality - the type of physical implementation or architecture used to create and manipulate qubits, the most fundamental unit of a quantum computer. Reference: Bank of America Institute

This week, Google Quantum is expanding its research into neutral atom quantum computers, which use atoms without an electrical charge as qubits. Neutral atom qubits are known for their flexibility and scalability, but additional research is required to enable them to perform longer sequences of quantum operations.

This is significant because until now, Google Quantum focused primarily on another type: superconducting qubits, which are fabricated electrical circuits that behave like artificial atoms when cooled to extremely low temperatures.

By expanding research into another type, it has sparked a conversation that superconducting qubits are too difficult to scale and productize.

However, Yossi Matias, Head of Google Research, insists that the company is betting on multiple qubit modalities, different physical implementations or architectures used to create and manipulate qubits. In the future, more companies may expand their research and development into multiple modalities rather than focusing on just one.

Other well-known qubit modalities include the following, as defined by Microsoft in this reference.

1. Trapped ion

2. Photonic

3. Topological

4. Quantum dot

5. Diamond nitrogen-vacancy (NV) center

6. Nuclear magnetic resonance (NMR)

This visualization is a great resource that provides an overview of each modality, found on the fourth page of a recent academic paper on fault-tolerant quantum computers.

Here are two graphs: one of private companies and private research organizations, and one of universities and public research organizations pursuing research and development for each quantum computing modality.

🛠️ Open-source of the week

DIY your own quantum computer

Open Quantum Design (OQD), a nonprofit organization that aims to develop a full-stack open-source quantum computer design in partnership with the University of Waterloo (Canada), has released its first hardware designs and their documentation.

Such open-source designs aim to reduce costs and democratize the production of quantum computers.

OQD focuses on trapped-ion quantum computers, a modality that uses laser-cooled atoms confined by radio-frequency electric fields inside an ultra-high-vacuum environment.

I was able to load the CAD file of the entire blade trap assembly, the hardware that generates the electromagnetic fields that confine these atoms. Though this could reduce the cost of producing a quantum computer, the actual system can’t simply be “3D-printed.” Building a working system requires vacuums and optics that are not readily available to the public.

Source (real blade ion trap): Oxford University

Another release in DIY quantum computing was Qilmanjaro’s EduQit, a full quantum computer kit you can assemble yourself.

A DIY quantum computer is interesting and a valuable educational tool, but it’s impractical today from a technical perspective. EduQit costs over 1 million USD to secure and 10 months to assemble, with a 3-month training period. Yet, it only has 5 qubits, which is not enough to run any practical algorithm.

🧰 Resource of the Week

Ethereum Foundation’s New Post-Quantum Roadmap Website

The Ethereum Foundation launched a new website detailing quantum vulnerabilities and the post-quantum migration roadmap for Ethereum, the second-most-popular blockchain.

If you've been following my Substack for a while, you know that post-quantum migration for blockchains is a topic I’ve covered extensively, so I won’t repeat the same points here.

Instead, here are some of the most useful snippets from the FAQ that go beyond the commonly discussed topics.

Is quantum risk primarily a cryptography problem or a systems-design challenge?

Choosing a post-quantum algorithm is only part of the challenge. The harder parts include safely upgrading hundreds of millions of accounts, preventing the migration from introducing new bugs, avoiding new attack surfaces, maintaining performance, and coordinating ecosystem-wide adoption.

Which risk surfaces are most concerning under future quantum capability?

In order of priority:

1. User accounts (EOAs): largest pool of value, public keys exposed after first transaction.

2. High-value operational keys: exchanges, bridges, custody hot wallets.

3. Governance and upgrade keys: admin multisigs controlling protocols.

4. Validator keys: affect consensus participation rather than directly holding assets.

This question assumes that users will need to manually migrate to post-quantum cryptographic keys, when they become available on Ethereum:

What about long-dormant funds and abandoned wallets?

Two natural scenarios exist: do nothing, or freeze vulnerable coins. Unlike Bitcoin, where roughly 5% of the supply is associated with early address formats widely believed to be abandoned (including Satoshi's ~1M BTC), Ethereum's exposure is closer to 0.1%.

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Other highlights this week include:

📰 News

• The Ethereum Foundation faced criticism after stating its Q-Day, the day when quantum computers are powerful enough to break popular encryption schemes, as 2032, while Google updated its to 2029.

• When faced with these debates, it’s important to recognize that each company has its own methodologies when predicting Q-Day.

  • In a previous Post-Quantum Roundup, I mentioned that each Q-Day prediction has its own methodology, with some sensational predictions basing it on the fewest qubits possible and the major assumption that qubits scale linearly (they don’t).

  • Another important point is that each company has different use cases and products, leading to varied attack vectors that are easier or harder for a quantum computer to break, as explained in this X post:

• Your new Android phones will be more quantum secure. Google announced that Android 17 (The current version is Android 16) would support post-quantum cryptography in two ways:

  1. Android Verified Boot, which is used upon device startup to ensure the code executed is from a trusted source, will use the ML-DSA signature scheme.

  2. Devices must use a PQC-compliant architecture for remote attestations to verify that the device has not been tampered with.

• Seven scientists advanced to the third round of the Quantum for Bio competition, which offers a $5 million prize for developing breakthrough healthcare algorithms using a quantum computer within these limits: 100-200 logical qubits and 100,000-10,000,000 gates.

  • The limits are intended to prevent algorithms that are impossible to run, as 100 logical qubits and 100,000 physical qubits are the specs for a “minimally” practical quantum computer. Here’s a recent short video explaining how to get these numbers:

• The UK government stated that it would not repeat the mistakes that led to its AI talent leaving for the US and would ensure quantum computing talent stays.

  • I’m beginning to see a growing belief that other nations want to capitalize on the quantum revolution before the US and China completely take over the industry, as they did with AI.

    • Canada announced a $900 million fund for defense and quantum technology innovation.

    • Yet, I’m confused about why Italy needed an anti-trust probe, in fear that quantum computing is getting heavy investment from and for only a few players.

• Congratulations to Gilles Brassard and Charles H. Bennett for winning the prestigious 2025 ACM A.M. Turing Award and for their contributions to advancing quantum computing.

🚀 New Opportunities

Check out QubitSok if you are looking for a job in quantum computing, found via The New Quantum Era podcast, which is excellent for keeping up with the quantum ecosystem.

I’m developing a website that simplifies finding research, internship, and education opportunities I've gathered, instead of creating a lengthy roundup.

The Post-Quantum Roundup is now sponsored by VoxBee, a privacy-focused, one-time-fee speech-to-text app for macOS and Linux. It stores data locally and is an affordable alternative to WisprFlow.

Standalone quantum computers won't define the near-term future — hybrid quantum-HPC systems will.

This Post-Quantum Weekly Roundup highlights a popular term used this week: high-performance computing (HPC), also known as supercomputing. It also outlines industry progress that signals greater adoption, including new tools and universities buying quantum computers, as well as growing government research and funding.

Make sure to check out my recent longer-form content, too.

📘 Definition of the Week

High-performance computing (HPC), also known as supercomputing, refers to an infrastructure that uses powerful computers, such as combinations of GPUs and quantum computers, to process massive data sets and solve complex problems at extremely high speeds in parallel.

Quantum-centric high-performance computing, or quantum-centric supercomputing, is the use of both a quantum computer and a traditional high-performance computer (such as a GPU).

This week, IBM launched a reference architecture map of quantum-centric high-performance computing, with its quantum computing stack as the focal point.

The idea is that quantum computers cannot replace traditional computers, as they are not efficient or practical for certain tasks in large-scale projects. Traditional computers can rely on quantum computers to handle tasks that are beyond their computational capabilities.

In a recent experiment modeling iron–sulfur molecules, a RIKEN Fugaku supercomputer coordinated the workflow, while a 156-qubit IBM Heron quantum processor sampled the molecule's quantum states. Fugaku then processed those measurements to compute the electronic structure.

Quantum-centric HPC is increasingly becoming a preferred architecture, as evidenced by the following news coverage.

• IonQ and the Korean Institute of Science and Technology Information (using IonQ quantum computers and NVIDIA GPUs)

• QuEra Computing emphasized that a state quantum computing program must align closely with local data centers that host GPUs and CPUs, as quantum computers need them

• This week’s NVIDIA GTC Conference in San Jose, CA, includes a plethora of sessions and announcements on using NVIDIA’s GPU and AI infrastructure with quantum computers. First, Pasqal and PsiQuantum join as one of the quantum computing providers for NVIDIA’s CUDA-Q platform. NVIDIA CUDA-Q is an orchestrator for applications that need an HPC infrastructure and distributes workflows across GPU, CPU, and QPU resources.

If you're seeking a more technical overview of quantum-centric HPC, I recommend this recent video:

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📚 Education

• Citigroup published a primer for business executives on quantum threats, their impact, and potential solutions. Send this to your CEO, your CFO, or any board member who keeps asking, "Do we really need to worry about quantum computing?"

📰 News

• APS Global Physics Summit 2026 is in Denver this week, so be on the lookout for major announcements from quantum computer companies. More updates in next week’s roundup.

• Researchers at Johns Hopkins University received a U.S. government grant to develop methods for keeping quantum computers running even when an attacker can tamper with them.

  • We heavily focus on how attackers will use quantum computers to break systems, but not on what attackers might do to quantum computers themselves. As quantum computers become more mainstream, this research will become much more important.

• The UK government announces it will spend up to 2 billion pounds on quantum computing research. This is significant, given that:

  • Cambridge, Oxford, and Glasgow were among the top 10 global quantum tech hubs in a recent report.

  • The UK is the second European nation, joining France, to actively want to win the quantum race. Could early investment in quantum computing help Europe regain its tech competitiveness?

    

• Universities are still the primary early adopters of quantum computers:

  • IonQ will install a 256-qubit quantum computer at the University of Cambridge in the UK. No estimated date confirmed.

  • IQM installs a quantum computer at Aalto University in Espoo, Finland

🔧 Technical

• Create, run, and deploy quantum circuits using natural language with YC-backed Coda. They also track their SLA metrics of their quantum computing cloud providers (IBM, IQM, IonQ, AQT) in a dashboard:

• IBM Quantum Platform updated its free plan. New signups will now receive 180 free minutes of runtime with a quantum computer for their first 12 months. Existing accounts already get 10 free minutes per month.

• A great overview of quantum “software development,” including what it means, approaches, and the tools/languages by Sara A. Metwalli, a post-doc quantum computing researcher currently based in the UK.

  • Recommended if you work in software and want to understand how quantum programming differs from classical.

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🚀 New Opportunities

Startups/Companies

• DARPA is inviting quantum companies with new technical architectures to join its rigorous, independent evaluation program, which includes IBM, IonQ, Microsoft, and more. Apply by July 31, 2026.

• The U.S. Federal Aviation Administration is requesting that cybersecurity and defense companies, regardless of size, submit information on how to transition their systems to post-quantum cryptography. Submit by April 10, 2026.

• IBM and Cisco opened a request for proposals for the design and realization of low-noise microwave-to-optical quantum transduction. Apply ASAP.

Academia

• Speaking of HPCs, if you are working on a research project, Q-Works is hosting the 1st workshop on Quantum-HPC Workflows, Resource Allocation, and Scheduling during Euro-Par 2026 in Pisa, Italy. Papers due May 15, 2026.

• CQT Hackamonth is a month-long, expenses-paid collaborative experience where PhD and postdocs from around the world work on quantum computing problems. Apply early by March 24, 2026. The late deadline is March 31, 2026.

• The Brookhaven National Laboratory is looking for paid undergraduate teaching assistants for their QIS 101: Foundations of Quantum Information Science summer program. Apply ASAP.

The full opportunity list this week is only available to paid subscribers.

Read more

Instead of a broad Post-Quantum Roundup, I’m trying out a new format that focuses on a trending topic of the week(s) with links and bite-sized explanations.

The Post-Quantum Roundup is now sponsored by VoxBee, a privacy-focused, one-time-fee speech-to-text app for macOS and Linux. It stores data locally and is an affordable alternative to WisprFlow.

🔓 Known vulnerabilities

Instead of only acknowledging that blockchains are not quantum-resistant, blockchain leaders are identifying specific vulnerability areas.

Vitalik Buterin, the founder of Ethereum, highlighted known vulnerabilities of the Ethereum protocol in a recent X post.

In turn, this graph by marilyn100x.eth explains these areas by mapping them to the specific blockchain operation that relies on them.

1. Users sign wallets to approve transactions that they want to make (EOA signatures (ECDSA)

2. Validator nodes sign to confirm transactions (consensus-layer BLS signatures)

3. L2s that use zero-knowledge proofs to handle transactions off-chain to save on gas fees and compress data for faster verification (Application-layer ZK proofs (KZG or Groth16)).

4. A missing piece: Transaction data is verified using cryptographic proofs, making it accessible to all nodes without requiring them to download the entire dataset (data availability (KZG commitments+proofs)).

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🚧 Known challenges and proposed solutions

Based on their strawman roadmap released in late February, the Ethereum Foundation estimates that full post-quantum migrations across all key areas will be completed by 2029

This is due to the technical complexity of research and implementation, which includes migrating to a post-quantum signature scheme, establishing a registry of post-quantum keys, and issuing post-quantum attestations (digitally signed statements).

Another visualization of Ethereum’s “Strawmap,” ETH2030, shows the sheer volume of tasks.

The main known challenges include:

🧺 Lack of signature aggregation

No post-quantum signature scheme supports aggregation, used in Ethereum to manage block sizes and verification latency.

On Ethereum, nearly one million validators sign to agree on the formation of a block of transactions. Instead of storing each signature, the BLS signature scheme, which is not quantum-secure, enables aggregating millions of signatures into a single one, which is then included in the final block.

According to a recent , the Ethereum Foundation is developing leanSig, a hash-based, post-quantum multi-signature scheme that uses SNARKs to aggregate signatures.

The current properties of leanSig, as further outlined by Thomas Cortager, researcher at the Ethereum Foundation:

1. leanSig will be hash-based, meaning that millions of public keys can be derived from a single main key by repeatedly hashing to form a hash chain. The number of hashes to set remains an open research question, as too many will impede performance. Currently, the only NIST-approved hash-based, post-quantum cryptography scheme is SPHINCS+.

2. Each validator can sign only one public key and one private key, a property known as One-Time Signatures.

3. Each validator will maintain a Merkle Tree, publishing the public keys they used to sign, so anyone can verify that a public key corresponds to a given validator.

4. A SNARK is used as the signature aggregator to verify the validity of a long list of signatures.

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🤸 Flexible cryptographic design

From Week 7:

Cryptographic agility, which is the ability to swap out signature algorithms without breaking all existing blockchain infrastructure.

Researchers are increasingly highlighting crypto-agile solutions, especially if current post-quantum solutions need to be replaced later as quantum computers advance. This quote from a forum post on Ethereum Magicians emphasizes the need for modular solutions:

Eli Ben-Sasson, an early research contributor to SNARKs and founder of Starknet, a Layer 2 blockchain solution on Ethereum, remarks that account abstraction is a valuable solution.

Previously, users relied on externally owned accounts controlled by private keys. Now, with account abstraction, accounts can be smart contracts with built-in logic for transaction authorization and execution, including using post-quantum cryptography.

EIP-8141 - Frame Transactions

Vitalik calls EIP-8141 an extension of account abstraction. Instead of requiring ECDSA, this proposal allows accounts to use their own cryptographic validation rules, as long as they use some cryptographic scheme.

This demo clearly shows how it would work, without changing the user experience.

I created a wallet on my MacBook using Touch ID as the authentication method, sent 0.1 ETH to another user, confirmed using Touch ID, and then, in the background, the signature generated by the Touch ID (WebAuthn P256 signature) confirms that the transaction was approved by the user.

In the future, this wallet could allow a user to approve transactions with a post-quantum signature.

Other Ethereum Improvement Proposals to follow:

• EIP-6404: SSZ transactions that use the EIP-7932: Secondary Signature Algorithms rails: replace the current transaction format with Simple serialize (SSZ), making it easier to verify transactions with new cryptographic algorithms.

• EIP-8164: Native Key Delegation for EOAs that acts as a foundation for PQ migration.

🎁 Bonus: Incompatible math

Post-quantum cryptography doesn't rely on the same math as Elliptic Curve Cryptography, which is necessary for non-hardened, software-based wallets.

Such schemes, like ML-DSA, round the public key during key generation. Using a rounded parent public key makes it impossible to determine the correct rounded child public key.

On Bitcoin, which still uses much of the same cryptography as Ethereum, Project Eleven created a wallet using the post-quantum RACOON signature scheme, which NIST hasn’t finalized yet. Their paper and blog post are now available.

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Behind the scenes of the Internet, public-key cryptography (i.e., RSA, Diffie-Hellman, and Elliptic Curve Cryptography) protects data like passwords and payment details from being read by anyone as it travels across the network. The development of quantum computers capable of breaking public-key cryptography requires a new Internet infrastructure.

Post-quantum upgrades to browsers and security protocols have been ongoing, but recent announcements about protecting the Internet from quantum computing have reignited questions about what else needs to be done.

Last week, Google revealed that it is taking the first step towards quantum-resistant website identification, starting by upgrading its TLS certificates to better support post-quantum signatures. Cloudflare’s new platform shows that post-quantum encryption adoption for Internet data transfer remains limited.

A fully quantum-safe Internet is still a work-in-progress. This article describes and explains how quantum-safe cryptography works and the current progress in implementing it.

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Current security guarantees of the Internet

The existing Internet infrastructure currently provides security guarantees we expect when using the Internet, such as:

1. Only the final website has access to sensitive data, such as passwords and payment details, when entered.

2. The website they are visiting is legitimate and not a fake version. For instance, Facebook.com is Meta’s social media platform, and hackers cannot alter the website domain to another site.

However, this was not always the case. Before the widespread adoption of security protocols that use public-key cryptography, such as SSL/TLS in the late 1990s, anyone on the same network could detect other users’ activity, including their usernames and passwords used for login.

Lookalike websites without SSL certificates, or using HTTPS, tricked users into logging in and intercepted their logins to real websites.

A quantum computer that can break public-key cryptography could revert the Internet to the insecure days of the 1990s. To ensure current security guarantees, quantum-resistant cryptography must replace the current public-key cryptography that secures the Internet.

How to quantum-secure the Internet

Any new, post-quantum infrastructure must maintain the same security without impacting the user experience in these key areas:

1. Connecting to a secure website

2. Identifying a legitimate website

3. Protecting sensitive data

Connecting to a secure website

The underlying process that a browser uses to connect to a website heavily relies on cryptography that needs to be upgraded to a post-quantum alternative. The adoption of post-quantum alternatives is increasing, but more action is needed.

How a secure website connection works

To establish a secure connection for transmitting sensitive data to the website, the browser and web server must complete a TLS handshake to agree on the encryption keys. A quantum computer could break the public-key cryptography that generates these encryption keys, generate the keys itself, impersonate the other party, and read sensitive data being sent between the browser and the web server.

The graph shows each step of the TLS handshake and how a quantum computer could compromise cryptography, enabling it to impersonate parties and generate encryption keys for a secure connection.

At a high level, the client and server use non-quantum-resistant public-key cryptography to exchange information and agree on encryption keys. A client, such as a web browser or an API, sends its information, including to the server. The server creates a secret from both its and the client’s info, which is never sent back. The server then sends its identity info to the client. The client verifies this and creates a secret based on it. These secrets generate the encryption keys.

Using post-quantum solutions to securely connect to websites

Instead of using public-key cryptography, such as Elliptic Curve Diffie-Hellman (for example, X25519), to generate the shared secret, clients and servers can use post-quantum key agreement schemes, also known as key exchange algorithms.

Clients and browsers are selecting X25519MLKEM768 as their preferred option, a hybrid solution that blends traditional elliptic-curve (X25519) and post-quantum cryptography (ML-KEM). It is the most adopted post-quantum solution as it offers backup security if one scheme is compromised and is more efficient than fully post-quantum alternatives.

In Steps 2 and 4 of the TLS handshake, the client and server each generate two secrets: one using the traditional X25519 scheme and another using the post-quantum ML-KEM. The final secret is the concatenation of the X25519 and ML-KEM shared secrets.

The main assumption is that a quantum computer cannot break both schemes simultaneously. A quantum computer would need to correctly guess both the X25519 and ML-KEM secrets between the same browser and web server, which is very hard.

Since X25519MLKEM768 uses both schemes, it requires more data to be transmitted and slows the TLS handshake; it still remains more efficient than fully post-quantum options, which adds to its popularity.

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Researchers found X25519MLKEM768 is about 0.0025 seconds, or 20 percent, slower than X25519, but it is still not as noticeably slow by several orders of magnitude as post-quantum options, such as MLKEM768 and MLKEM1024 [1]. In practice, the Chrome team observed an average latency of four percent across all TLS handshakes with X25519MLKEM768, which they considered negligible for their users [3].

Adoption of X25519MLKEM768

The adoption of X25519MLKEM768 is progressing slowly: clients are adopting it quickly, but web servers have not yet.

The latest versions of most browsers, including popular ones such as Chrome, Firefox, Safari, Brave, and Edge, already support X25519MLKEM768.

The adoption of post-quantum cryptography on servers is much, much lower. Currently, only 8.6 percent of servers use X25519MLKEM768, up 3.4 percentage points from the previous year.

This disparity in adoption between clients and servers is technically a challenge, as both must support the same post-quantum cryptography scheme for it to work; otherwise, they will need to default to another supported scheme, potentially a non-post-quantum one. Ideally, web servers should adopt post-quantum cryptography because, without it, the connection between the origin server and reverse proxies will be insecure.

Fortunately, most web servers rely on intermediary services that use post-quantum cryptography. These intermediary services, known as reverse proxies, are servers that sit in front of original web servers and manage, secure, and accelerate incoming user traffic, including generating secrets and establishing secure connections with clients.

Popular reverse proxies such as Cloudflare and AWS CloudFront use X25519MLKEM768 to generate post-quantum-secure secrets. Upon connecting to the latest popular browsers, they can establish secure browser connections on behalf of the original web server.

For example, since the host of substack.com supports X25519MLKEM768, your connection to Substack remains post-quantum secure as long as you use an updated browser.

In turn, 65.7 percent of HTTPS traffic is already quantum-secure, as most intermediary services and browsers have implemented post-quantum cryptography.

However, that means one-third of Internet requests are currently not quantum-secure, indicating that much more adoption of X25519MLKEM768 is still needed.

Identifying legitimate websites

Unlike using post-quantum cryptography for web connections, applying it for website authentication noticeably slows down the experience and, therefore, is not widely adopted.

In Step 3 of the TLS Handshake in Figure 4, the server provides a certificate that verifies its identity, proving that it is the server for the specific domain, before the client can proceed to establish a secure connection. The certificate includes a public key and a signature that the client can use to verify that the signature is associated with the public key.

Currently, certificates are signed using the Elliptic Curve Digital Signature Algorithm (ECDSA), which is not quantum-resistant (You can read my previous article on ECDSA here).

The challenge with using a post-quantum signature scheme is its slowness and the need for more certificate storage.

Creating and verifying post-quantum signatures is slow, slowing down the TLS Handshake process. Cloudflare and independent research teams found that using a post-quantum signature scheme increased TLS latency by 20 to 40 percent [2, 3]. Chrome adopted X25519MLKEM768 for web connections because it only added four percent latency, but it avoids further quantum security by adding post-quantum signatures to certificates due to the substantially higher latency [3].

Another challenge is that post-quantum signatures are more than 30 times larger, requiring much more storage for certificates on web servers and certificate management platforms.

Google plans to solve the problem of signature sizes by introducing Merkle Tree certificates, with a finalization plan by Q3 2027. Instead of storing the signature directly in the certificate, they would be stored in separate Merkle Trees.

The certificate stores a Merkle proof, a cryptographic method used to verify that a specific piece of data in a Merkle Tree.

A standard ECDSA signature is 64 bytes. The smallest post-quantum signature is 2,420 bytes, and the Merkle proof that Google and its partners are initially reviewing is 734 bytes, making Merkle proofs a better alternative to replacing ECDSA [4].

Quantum-secure website identity and authentication will be slower than for the two other flows, as upgrading to post-quantum signatures is the most challenging aspect of a post-quantum Internet.

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Protecting sensitive data

The quantum security level of AES-128, the current method for encrypting data sent between a client and a server, is often debated.

Using AES-128, the plaintext is encrypted with a 128-bit key, which a hacker would try to recover to decrypt and steal data.

Organizations such as the U.S. National Institute of Standards and Technology and Cloudflare do not consider AES-128 highly vulnerable to quantum computing.

Some organizations, like Cisco, recommend upgrading to AES-256, which uses a longer 256-bit key, making it more difficult for a quantum computer to crack and thus providing better system protection. Although NIST does not recommend that all enterprises migrate, all U.S. government organizations and major cloud providers such as Google Cloud and Amazon Web Services already use AES-256.

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Conclusion

A quantum-safe Internet has advanced steadily, with the flows ranked by the most post-quantum adoption:

1. Connecting to a secure website (High)

2. Protecting sensitive data (Some already consider it post-quantum secure, while others do not)

3. Identifying a legitimate website (Low)

Browsers and reverse proxies commonly use X25519MLKEM768, a hybrid key agreement scheme that combines traditional and post-quantum methods, enabling websites to set up secure connections.

Many organizations believe that using AES-128 for data encryption on the Internet is already quantum-secure, but some push for migrations to higher-security AES-256.

The most significant challenge with a quantum-safe Internet is migrating to post-quantum signatures, which servers use to authenticate and prove their identity to clients such as browsers and APIs. Potential solutions, such as Merkle Tree Certificates, must address the slowness and high data storage requirements of post-quantum signatures.

Additional Sources

1. Mrinal, K., & S, V. (2025). 2025 9th International Conference on Computing, Communication, Control and Automation (ICCCBEA). In IEEE. Retrieved March 6, 2026, from https://ieeexplore.ieee.org/document/11283923.

2. Sikeridis, D., Kampanakis, P., & Devetsikiotis, M. (2020, February 26). Post-quantum authentication in TLS 1.3: A performance study. IACR Cryptology ePrint Archive. https://eprint.iacr.org/2020/071

3. Chromium. (2024, May 23). Advancing our amazing bet on asymmetric cryptography. Chromium. https://blog.chromium.org/2024/05/advancing-our-amazing-bet-on-asymmetric.html

4. Benjamin, D., O’Brien, D., Westerbaan, B., Valenta, L., & Valsorda, F. (2026, March 2). Merkle Tree certificates. IETF Datatracker. https://datatracker.ietf.org/doc/draft-ietf-plants-merkle-tree-certs/

The Post-Quantum Weekly Roundup prepares technologists for the quantum computing revolution and post-quantum world.

This week’s roundup doesn’t necessarily have a direct “theme,” other than that it covers the various touchpoints and conversations in quantum computing and post-quantum cryptography I’ve encountered through my research.

A special announcement: Realmscape is becoming more accessible to everyone through its newly launched subscriber referral program. When you use the “Refer a friend” link below, or the “Share” button on any post, you’ll get credit for subscribers to the publication.

Refer a friend

When your friends subscribe through your referral link, you’ll receive special benefits:

• Get 1 month paid membership for 3 referrals

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• Get 6 months paid membership for 25 referrals

Definition of the Week

Distributed quantum computing enables multiple quantum computers to collaborate over a network.

Current quantum processors have 100 to 1,000 qubits, but impactful algorithms need hundreds of thousands or millions. Distributed quantum computing connects multiple processors to scale up the number of qubits instead of building a single large processor.

Shared by last week’s QuantumX talk at the University of Washington, one example of distributed quantum computing is connecting dilution refrigerators that store quantum processors via a waveguide or a conductive metal pipe that confines and guides electromagnetic waves, as shown below:

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Conversation of the Week

With Jay Jog, founder of Sei, an Ethereum-compatible (EVM), specialized Layer-1 blockchain known for parallelized transactions.

If you are looking for more context on Sei, I previously wrote an article on parallel execution on EVM chains, highlighting them and Monad:

Jay highlighted, as a key takeaway at Ethereum Denver last week, that:

Nobody is preparing fast enough for quantum computing

I asked him what Sei’s plans were for post-quantum migration, and he responded with the following:

In other words, he believes that Sei will need to migrate only to a post-quantum signature scheme and that there are no other quantum vulnerabilities. The challenge in migrating to popular post-quantum signatures (like Dilithium, FALCON, Sphincs+, per my latest long-form article) is that their sizes are 20-40x larger than current signatures.

The next challenge is to find a user-friendly flow for users to “claim” their quantum-safe public/private key pairs. One way is that once a signature scheme is selected and migrated to, users will likely need to associate their current public/private key pair with the new quantum-safe public/private key pair by submitting a transaction. 

Video/Podcast of the Week

A interview with Justin Drake, a researcher at the Ethereum Foundation who is leading its post-quantum cryptography migration.

Justin Drake also emphasizes that the main difficulty with post-quantum cryptography is that its signatures are much larger.

On Ethereum’s consensus layer, where nodes agree on the transactions, 32,000 signatures are made per slot per epoch (almost every second). BLS, the current consensus layer signature scheme, is 92 bytes, while post-quantum cryptography signature schemes are around 1 kilobyte, which is 10 times larger.

Such a huge increase in signature sizes would significantly slow down bandwidth and verification time on Ethereum, requiring off-chain solutions to handle and prove signatures such as zero-knowledge proofs.

Runners-up for video/podcast of the week:

“Which Cryptos Will Survive Quantum?” — Unchained Podcast with , Chris Peikert (University of Michigan), and Justin Drake (Ethereum Foundation).

A key insight identified was that areas of the Ethereum blockchain currently using quantum-prone Elliptic Curve Cryptography need to be updated to post-quantum cryptography.

• User transactions use ECDSA

• Consensus and verification of transactions use BLS signatures

• Data layer uses KZG

“Has Bitcoin Already Done 'a Lot of Work' on Quantum? Yes, Says One Core Dev” — Unchained Podcast with and Matt Corallo (major contributor to Bitcoin Core).

ECC Has an Expiry Date, Post-Quantum Cryptography Fixes It — Danno Ferrin ()

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Education

• Qiskit Seminar Series restarts on Friday, February 27th, with a new video by Professor Martin Savage of the University of Washington (Seattle), who will discuss his research on understanding the properties of matter using quantum computers, crucial to material science, drug discoveries, and more. Subscribe to the Qiskit YouTube channel.

• Build your first quantum support vector machine, a free virtual course on quantum-based support vector machines (SVMs), which supervised machine learning algorithm that classifies data by finding an optimal line. Register by the course time on Tuesday, March 3rd, at 8:00 AM PST.

News

• French President Emmanuel Macron bets on quantum computing as a key technology, predicting that France will be a global leader in the field by 2035.

• Comcast partnered with Classiq to develop and run a quantum algorithm on an AMD GPU, optimizing and rerouting network traffic to alternative sites during maintenance and downtime.

  • You might be thinking: How do you run a quantum algorithm on a GPU? The short answer is quantum simulators, software programs that run on classical computers and can reproduce results from a quantum computer. It’s the topic of my next long-form article.

• RIKEN's supercomputer Fugaku and IBM's Quantum Heron processor together calculated the electronic structure of a pair of complex iron-sulfur molecules.

  • This is an example of quantum-centric supercomputing, or when classical supercomputers (tens of thousands of high-quality GPUs and CPUs) and quantum computers work together to solve a problem.

  • Practical questions that arise from this kind of research include: What is the value of quantum computers if we have supercomputers? Or need to work closely with supercomputers?

  • It’s a valid question that even Hossenfelder, a famous scientist YouTuber, asked in one of her videos this week. What do you think?

• IBM Ventures invested in two quantum early-stage companies through the Alchemist Accelerator in Chicago: SQK and QCodeX Quantum.

  • SQK uses quantum algorithms for medical image reconstruction (MRI scans to 2D/3D images).

  • QcodeX Quantum enables quantum-native AI models.

Technical

• Cloudflare launched the first SASE with modern post-quantum encryption.

• PsiQuantum Circuit Designer is a free tool for creating and sharing quantum circuit diagrams, such as this double factorization circuit:

  

• Classiq, a full-stack quantum programming tool, released its first production version (Version 1.0).

Opportunities

Hackathons

Credit to NucleiQ for many of these opportunities!

• The Unitary Design Challenge, a virtual design hackathon from February 16-27, 2026, that encourages people to contribute to the open-source quantum ecosystem through the lens of community engagement and science communication.

• We in Quantum Development (WIQD) Hackathon 2.0 at TU Delft, Netherlands, March 13, 2026

• Open Quantum Institute Hackathon in Morocco, May 12-14, 2026

• Quantum Impact Hackathon in Rabat, Morocco, June 23-25, 2026

• QC4SG Vietnam 2026 - The 2nd SEA Quanthathon in Gia Lai, Vietnam, Jul 24-28, 2026

Conferences

• Texas Quantum Economy Conference in Richardson, Texas, USA on Saturday, February 28th

• Pitch session of finalists of the Berlin Quantum Hackathon, March 5, 2026.

The full list of opportunities is available only for paid subscribers. Upgrade to paid or refer a friend to start accumulating points towards a free paid subscription.

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The Post-Quantum Weekly Roundup prepares technologists for the quantum computing revolution and post-quantum world.

This week’s post-quantum roundup focuses on demystifying quantum risk. While I believe in quantum risk, I’m still concerned about the rise of overexaggerations and broad claims among quantum “influencers.”

Also, I’m finally back in Seattle after traveling and visiting family over the past few weeks. Speaking of traveling, the European Centre for International Political Economy recently published a new ranking of 86 quantum computing hubs worldwide. Which quantum hub would you like to live in (or do you already live in)?

My picks are San Francisco (a great startup ecosystem), Helsinki (a safe city), and Seoul (a great culture. I love their music!)!

Definition of the Week

Mosca's theorem, developed by Dr. Michele Mosca of the University of Waterloo in Canada in 2015, explains the severity of quantum risk. The theorem has been cited more frequently in the past few months as quantum risk has become more severe.

The theorem states that cryptographic secrets break when:

The total duration in which the data must stay secure (x), plus the time needed to migrate to quantum-proof systems (y), exceeds the time required to develop a cryptographically relevant quantum computer (CRQC) (z), or a quantum computer that can efficiently break widely used public-key encryption.

We should worry because a CRQC will be available before all systems are migrated, and standard cryptography will start to fail when:

x + y > z

We should actively work toward post-quantum migration, but we have buffer time until cryptography fails, when:

x + y < z

Suppose a hospital encrypts patient genomic data today using RSA and must keep it confidential for 20 years due to privacy regulations and long-term sensitivity. If it realistically takes 8 years to audit systems, update hardware, certify software, retrain teams, and fully migrate to post-quantum algorithms, then:

x = 20
y = 8
x + y = 28

If a CRQC capable of breaking RSA emerges in 15 years, as the U.S. National Institute of Standards and Technology (NIST) believes it will:

z = 15

Then 28 > 15, meaning that the genomic data will likely be leaked by hackers who will use quantum computers to break RSA encryption.

How do we actually know when a CRQC will be ready?

The direct answer is that we don’t, but we can still estimate.

Countdowns to when a CRQC will be ready, or “Q-Day” estimates, predict when a defined number of logical, error-free qubits, as claimed by specific academic research to be needed to break a popular cryptographic scheme, will be available, based on trends in the number of available logical qubits.

The challenges with this methodology are that:

1. Academic research varies on the defined number of logical, error-free qubits necessary. The range is 1,700 to 6,000 logical qubits to break RSA encryption, and sensational countdowns tend to pick the lowest number.

2. The number of available, logical qubits does not necessarily grow at standard rates.

Examples of Q-Day countdowns, which are four years apart in their estimations, and their varying methodologies:

• Quantum Doomclock - Methodology

• CRQC Readiness Benchmark (Q-Day Estimator) - Methodology

Quantum computers will advance, but how fast you think they’ll progress depends on the academic research you follow.

Academic Paper of the Week

Webster, P., Berent, L., Chandra, O., Hockings, E. T., Baspin, N., Thomsen, F., Smith, S. C., & Cohen, L. Z. (2026, February 12). The Pinnacle Architecture: Reducing the cost of breaking RSA-2048 to 100 000 physical qubits using quantum LDPC codes. arXiv.org. https://arxiv.org/abs/2602.11457

Researchers at Iceberg Quantum, a private company based in Sydney, Australia, that designs full quantum systems, claimed they can break RSA encryption with only 100k physical qubits using a new technical architecture, far fewer than the 900k qubits previously estimated in 2024.

Physical qubits are error-prone, while logical qubits are created by grouping physical qubits to protect them against errors and are more reliable for computation.

This article was widely shared within the post-quantum cryptography community as a major breakthrough, often without context. It’s an interesting finding, but without context, it can be misinterpreted.

What is Pinnacle Architecture, the new technical architecture approach that Iceberg Quantum uses?

Iceberg Quantum proposed Pinnacle Architecture, a full-system, modular design, built around quantum Low-Density Parity-Check (qLDPC) codes. qLDPC codes are a newer family of error-correcting codes designed to protect fragile quantum information using far fewer extra qubits.

Pinnacle Architecture separates the quantum computer into specialized components: memory blocks that store logical qubits, processing units that perform computations, and dedicated “magic engines” that generate the high-quality special states required for complex operations.

How do researchers know that this can be done with 100k qubits when 100k qubits do not exist?

Like much research, Iceberg Quantum’s work relies on software modeling rather than using quantum computers.

Researchers use quantum resource estimation, which involves software models that simulate the number of qubits needed for a specific task. For example, Microsoft’s free quantum resource estimation tool uses well-known predefined qubit parameter settings and common error-correcting schemes to estimate the number of qubits required for a task.

To calculate the energy associated with this chemical system within 18 minutes:

A nitrogen molecule where 10 electrons occupy the 8 orbital active space of the dissociated nitrogen at a 3 Angstrom distance

According to the Microsoft Azure Quantum Resource Estimation tool, it would require 207,604 qubits. 15 percent of qubits are dedicated to T-factories that produce T-states, which are valuable for low-error rates.

Adjusting the runtime, T-factory percentage, and other parameters could increase or decrease the number of physical qubits.

Researchers adjust the models to account for different error rates, operational speeds, and error-correction schemes. Understanding their methodology is important for assessing the likelihood of the result.

In the case of Iceberg Quantum, they used a model based on their pinnacle architecture, which was adjusted to different error rates and code cycles, or time to run a round of a quantum error correction code. They applied a quantum algorithm capable of factoring a 2048-bit RSA integer (or capable of finding two very large prime numbers whose product equals the RSA integer) to their qLDPC error-correction scheme and simulated the number of qubits required.

Using Shor’s algorithm, factoring an n-bit RSA number is known to take O(n³) gates. For a 2048-bit RSA integer, this typically meant 2048³ = 8.6 × 10⁹ gates, which required roughly 2,000-6,000 logical qubits and, under traditional error-correction assumptions, approximately 10–20 million physical qubits. Under Pinnacle Architecture, the breaking RSA required a similar number of gates and logical qubits, but qLDPC encoding reduced the physical qubit requirements, lowering the total to 100k physical qubits.

Runners-up for Academic Paper of the Week:

From the second breakout call on Post Quantum transaction signatures by the Ethereum Foundation:

Kudinov, M., & Nick, J. (2025, December 5). Hash-based signature schemes for Bitcoin. IACR Cryptology ePrint Archive. https://eprint.iacr.org/2025/2203

From PQCrypto 2026 accepted papers (which include many other great papers, too):

Centelles, A., & Mendelsohn, A. (2026, January 31). Abba: Lattice-based commitments from commutators. IACR Cryptology ePrint Archive. https://eprint.iacr.org/2026/148

Shared by :

Chevignard, C., Fouque, P.-A., & Schrottenloher, A. (2026, February 17). Reducing the number of qubits in quantum discrete logarithms on elliptic curves. IACR Cryptology ePrint Archive. https://eprint.iacr.org/2026/280

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Video of the Week

A interview with Thomas Coratger, researcher at the Ethereum Foundation (EF), where he explains the quantum threat to Ethereum and potential technical challenges Ethereum might face migrating to post-quantum cryptography.

Next week, I’ll explain the technical requirements that his colleague, Justin Drake, uncovers in another, more technical podcast that was recently released.

Education

• Quantum computing free online courses

• ARMChain is hosting an Introduction to Post-Quantum Cryptography webinar on Sunday, February 22nd, from 10:00 to 11:00 AM PST. Register here.

• Build your first quantum support vector machine, a free virtual course on quantum-based support vector machines (SVMs), which supervised machine learning algorithm that classifies data by finding an optimal line. Register by the course time on Tuesday, March 3rd at 8:00 AM PST.

New Opportunities

Virtual

• QFELLOWS is a flagship PhD and research community by Tectonic, a company building quantum-grade infrastructure for blockchains, that brings together quantum researchers, theorists, and experimentalists across disciplines to accelerate breakthroughs in post-quantum technology.

  • If you are interested in joining this community, please let me know if you want an introduction to the Tectonic team, as I am part of it!

• Girls in Quantum Q-Hackathon 2026. For female students and researchers to create quantum projects in four tracks: Hardware (Energy Grid Optimization), Algorithm (Harmonic Oscillator), Finance/Quantum Machine Learning (Option Pricing), and Social Impact (Quantum for Good - no coding required in this track). Due: Apply by February 20 (Though the application says apply by February 23rd at 11:59 UTC).

Geography-specific

• QIS 101: Foundations of Quantum Information Science is a six-week summer virtual program that introduces U.S. undergraduate and graduate students, recent college graduates, and academic educators to quantum information science and pays them a $500 weekly stipend for active participation. Due: Apply by April 3, 2026.

• NQN Northwest Quantum Day in Seattle, Washington, USA, on Tuesday, April 14th, is a conference on the quantum ecosystem in the U.S. Pacific Northwest region. Come say hi if you are in town!

• The Quantum Un-conference in Cambridge, MA, USA, on Saturday, February 21st, is a gathering of collaborative discussions on quantum computing. No speakers, only attendee collaborative discussions and presentations on topics such as:

  • What is quantum computing?

  • Learn and teach any quantum computing topic

  • What is your favorite qubit?

• Following the Quantum Un-conference, the Sundai Quantum Hackathon in Cambridge, MA, USA, on Sunday, February 22nd, is a quantum hackathon with three unique challenge tracks:

  • Software (quantum algorithms)

  • Hardware

  • Physics (self-study the quantum mechanics behind quantum computing)

Previously shared opportunities

The full list of opportunities for paid subscribers.

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This article explains the importance of post-quantum signatures, lists the blockchains that use them, and describes the signature schemes they selected.

The full spreadsheet with sources, including marketcap references, documentation, and code links, can be viewed here.

I recommend a previous article if you are looking to understand why blockchains are not quantum-resistant.

Why focus on signatures

The most important step in securing a blockchain against quantum computing is migrating to a post-quantum signature scheme.

In the previous article, I explained the importance of signatures in a blockchain, especially for validating that a cryptocurrency transaction was initiated by a user.

A proposed transaction is then sent to a node or device permitted to send transactions to the specified blockchain.

When a node receives a transaction, it parses the data and pulls out the sender’s public key and the [current] signature. Then it re-hashes the transaction data or raw data and runs elliptic-curve math to verify that the signature matches the hash and the sender’s public key.

If everything checks out, the transaction is considered authentic and moves into the mempool, where it can later be included in a block by miners or validators. If it does not pass verification, the node rejects it right away.

As explained later, quantum computing could enable hackers to forge [current] signatures and send transactions without user permission, making it impossible for nodes to distinguish between fraudulent and legitimate transactions.

In other words, when Bob wants to send a cryptocurrency token to Alice, he uses his private key, which is analogous to a private bank account detail, to generate a signature.

Bob’s public address, or his public “bank details on the blockchain,” and his signature are then transmitted to the blockchain. A node, which is a computer that connects to the decentralized network and validates the blockchain’s transactions, uses cryptography to verify the signature, ensuring it matches Bob’s public address.

Compromising the signature scheme would enable hackers to send transactions without the user’s permission.

In the long term, quantum computers could break a standard signature scheme by generating and iterating through all possible private keys. Hackers can then create signatures using generated private keys with user funds and send those funds to their accounts.

Implementing a post-quantum signature scheme is the most important step toward securing a blockchain against quantum computing threats and is usually the first step most blockchains consider.

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As post-quantum security becomes a higher-profile narrative, some blockchains and protocols have highlighted use cases such as running quantum computers as nodes or using quantum-mechanical technologies that are not quite quantum computers, such as quantum random number generators. However, these use cases are less relevant if standard signature schemes are not quantum-proof.

Quantum-resistant transactions do not guarantee complete security

It’s important to note that a blockchain employing post-quantum signatures for transactions alone isn’t necessarily fully resistant to quantum attacks.

First, every post-quantum cryptography signature scheme carries its own implementation risks, as described in the Signature schemes selected section below.

Second, additional areas of the blockchain operations flow need to use post-quantum signatures. Nodes validate blocks of transactions using signatures; they must be able to sign with a post-quantum signature, not only read one. This requires a node client software upgrade and improved hardware and network infrastructure, as post-quantum signatures are larger and slower to validate [2].

Quantum-proof does not mean completely secure either. Blockchains are still prone to bugs at the protocol level (e.g., a smart contract vulnerability) and the app level (e.g., a third-party cryptocurrency exchange or wallet vulnerability), user error (e.g., users accidentally sharing their private keys), and scams.

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Therefore, please use the blockchains introduced below at your own risk.

Which post-quantum signature schemes are blockchains choosing

I define blockchains that use post-quantum signatures as follows:

1. Mentions at least one specific, academically-approved (approved by the U.S. National Institute of Standards and Technology (NIST) preferred), post-quantum signature scheme that is integrated in their whitepaper, documentation, and/or public code base

2. Made a post-quantum signature scheme transaction on its testnet (test-level) or mainnet (production-level)

3. Outlines a comprehensive, committed plan for implementing a specific post-quantum signature scheme.

   1. For example, Aptos released an improvement plan that highlights the use of accounts on Aptos with Sphincs+ as the transaction signature scheme.

I do not consider these blockchains as implementing post-quantum signatures:

1. Researching which post-quantum signature scheme(s) to migrate or integrate, but no firm commitment on which one(s) (sorry, Ethereum fans!)

2. Modular cryptographic chains, which are chains that claim to be built in a way that signature schemes can be easily swapped in or out. This is a valuable but very early vision for blockchains. Right now, blockchains still need to define which signature scheme(s) their nodes can handle, and all of these “modular cryptographic chains” still rely on non-quantum-proof elliptic-curve signatures.

I did not include AMEChain, Geeq, Qubitcoin, Abelian,

Post-quantum cryptography (PQC) blockchains

The full spreadsheet with sources, including marketcap references, documentation, and code links, can be viewed here.

A total of 12 chains met the criteria above and integrated post-quantum signatures:

• Algorand

• Aptos

• Quantum Resistant Ledger

• Nervos CKB

• QANPlatform

• Naoris Protocol

• QuantumCoin

• Minima

• Cellframe

• Tidecoin

• Bitcoin Quantum

• Quarnium

Lesser-known blockchains with smaller user bases, or those that are completely new, do not carry the same risk and technical debt as more widely used blockchains with millions of users, such as Ethereum and Bitcoin.

Smaller blockchains can more easily migrate to or integrate post-quantum signatures for transactions.

Blockchains that have implemented post-quantum signatures live on mainnet or in production have a median market cap of $9.53 million. Algorand, the most mainstream blockchain, ranked 74th in native token market cap (out of 18,000+ tokens), has a market cap of $790.81 million. Meanwhile, Ethereum's market cap stands at $234 billion.

Two blockchains (Bitcoin Quantum and Quranium) do not have a token, meaning they have no financial value tied to their use of blockchain. Naoris has a native token, but the production version of its blockchain has not yet been released to the public.

The median mainnet launch date is 2023, with the latest release date as 2018, which is quite new compared to older blockchains. Bitcoin was released in 2009, Ethereum in 2015, and even Solana, which is considered “new” by some blockchain users, in 2020.

Signature schemes selected

Number of blockchains by post-quantum signature scheme

Overview

The 12 blockchains integrated CRYSTALS-Dilithium/ML-DSA, Sphincs+, FALCON, Picnic, and Winternitz One Time.

CRYSTALS-Dilithium/ML-DSA, Sphincs+, and FALCON are the most popular, as the U.S. National Institute of Standards and Technology (NIST) selected them as the final three post-quantum signature schemes recommended for use.

The most popular signature scheme selected is CRYSTALS-Dilithium/ML-DSA, which is used by half or 6 of the 12 blockchains, and NIST recommends it as the primary post-quantum algorithm.

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Why each signature scheme was selected

This section explains why each signature scheme was selected by both the academic community and blockchain contributors.

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Lattice-based cryptography

Definition

CRYSTALS-Dilithium/ML-DSA and FALCON are signature schemes that are secured by difficult math problems based on lattices, infinite sets of evenly spaced points in space.

In a prior article on lattice cryptography:

Finding the shortest vector is simple in two or three dimensions, but becomes difficult even for a quantum computer in thousands or even infinite dimensions.

Selection

CRYSTALS-Dilithium/ML-DSA

Most PQC blockchains currently use CRYSTALS-Dilithium/ML-DSA because it is recommended by NIST as the primary algorithm.

The Quantum Resistant Ledger team specifically highlighted in a video primer:

NIST selected CRYSTALS-Dilithium/ML-DSA for robustness. Firstly, by reducing its signature sizes, it becomes highly efficient for generating and validating signatures. It has a straightforward implementation, strong security, and a favorable cryptanalytic record, or the absence of any known breaches, comparable to other post-quantum signature schemes.

FALCON

FALCON was selected by NIST for its strong security and, according to Algorand, is also “suitable for deployment in bandwidth-and latency-sensitive environments such as blockchain systems.”

Though FALCON generates signatures more slowly, its signature verification is faster and has smaller keys and signatures. Independent research studies show that a blockchain using FALCON-512 signatures, which are considered Level 1 (out of 5) and the lowest tier for post-quantum security, achieved the highest transaction-per-second rate, surpassing both Level 2 and the highest security-level versions of Dilithium.

Algorand has an additional competitive edge in integrating FALCON, as the cryptographers involved in its development are, or were, part of Algorand’s core research team. Dr. Zhenfei Zhang, a former Algorand cryptographic researcher, contributed to the design of FALCON. FALCON is based on a theoretical framework that Craig Gentry, a former Algorand Foundation research fellow, Chris Peikert, Head of Cryptography at Algorand Technologies, and Vinod Vaikuntanathan (MIT Professor) [2].

FALCON has downsides, though. It was selected behind CRYSTALS-Dilithium/ML-DSA and Sphincs+ because it is complex to implement, requiring floating-point arithmetic to represent real numbers in scientific notation [3].

Hash-based cryptography

Definition

Sphinics+ and Winternitz One-Time are signature schemes that are secured by hash functions, which “hash” information or take data and convert it into a unique, encrypted, unreadable output.

To send a transaction, the transaction data is first hashed to produce an output. To sign it, the signer reveals specific secret values that correspond to that hash. Those revealed values, along with additional proof data, form the signature.

Selection

Sphincs+

Sphincs+ was selected by NIST as a backup algorithm to CRYSTALS-Dilithium/ML-DSA.

NIST chose Sphinics because its security seems “quite solid” and is based on a different cryptographic basis than CRYSTALS-Dilithium/ML-DSA and FALCON [4]. However, it is a secondary algorithm, as its signatures are 120-300 times larger than typical current ECDSA signatures, which are widely used in many blockchains. Signature generation and verification are slower than those of lattice-based schemes [5].

Nervos addressed this downside by keeping signatures out of the persistent state, as do most other blockchains. However, Nervos is perhaps stricter about separating stored state from transaction proofs, and it discourages unnecessary storage by requiring users to lock funds for every byte they store. Signatures are checked for each transaction and not kept as part of the ongoing state.

Despite Sphincs+ having large signature sizes, Aptos and Nervos chose it because they believed its familiar technical foundation outweighed the drawbacks. Hash functions are already widely relied on and familiar to blockchain contributors, whereas other post-quantum signatures rely on unfamiliar assumptions that contributors might not trust or that are very hard to learn and integrate correctly.

Nervos also noted that Sphincs+ is more practical for blockchains because, unlike other hash-based cryptographic schemes, it does not require state management of used keys. Keys can be used again and again.

Winternitz One-Time

Winternitz One-Time is a simple signature scheme that is impractical on its own, as each key pair is used only once.

However, Minima combines it with a hierarchical data structure called Merkle Mountain Range hash trees, so users can use the same public key to receive funds and a different private key, used only once, to sign transactions. Even if a private key is exposed, the hacker cannot do anything, since it has already been used in a previous transaction and can be used only once.

Other post-quantum cryptography

Picnic is a signature scheme based on zero-knowledge proofs, cryptographic methods that enable one party to prove a statement is true without revealing extra information, rather than relying on hard mathematical problems. Cellframe uses it as Picnic keys are more “compact” than those from public-key cryptography.

Picnic was a finalist but did not proceed to the final round because it resembles Sphincs+ but lacks the same security standards [4].

Conclusion

Using post-quantum signatures is the most important step in securing a blockchain against quantum computing. A cryptographic signature scheme that is not quantum-resistant can reveal users’ private keys, allowing hackers to gain access to their accounts.

Currently, the 12 blockchains that have either migrated or have a concrete plan to migrate to a specific post-quantum signature scheme are smaller, lesser-known blockchains. Less popular blockchains have lower risk and greater agility, with a smaller, tight-knit user base and are usually newer, with less technical debt.

Half of the blockchains chose CRYSTALS-Dilithium/ML-DSA, as it is recommended by the U.S. National Institute of Standards and Technology (NIST) as the primary post-quantum algorithm. FALCON and Sphincs+ were the only other two signature schemes with more than one blockchain integration and were selected by NIST as the two other backup algorithms. FALCON and Sphincs+ also benefited from developer familiarity. In the case of FALCON, the research team at Algorand was integral to its development, and for Sphincs+, blockchain developers were already familiar with hash functions, on which it is based.

Additional Sources

1. Kalogeropoulos, A. (2018a, June 15). A Reference Architecture for Blockchain-based Resource-intensive Computations managed by Smart Contracts. ResearchGate. https://www.researchgate.net/publication/328342750_A_Reference_Architecture_for_Blockchain-based_Resource-intensive_Computations_managed_by_Smart_Contracts

2. Young, L. (2025, November 3). Technical brief: Quantum-resistant transactions on Algorand with Falcon Signatures. Algorand Foundation. https://algorand.co/blog/technical-brief-quantum-resistant-transactions-on-algorand-with-falcon-signatures

3. Kim, H., Kim, W., Kang, Y., Kim, H., & Seo, H. (2024). Post-quantum Delegated Proof of Luck for Blockchain Consensus Algorithm. Applied Sciences, 14(18), 8394. https://doi.org/10.3390/app14188394

4. Alagic, G., Apon, D., Cooper, D., Dang, Q., Dang, T., Kelsey, J., Lichtinger, J., Liu, Y.-K., Miller, C., Moody, D., Peralta, R., Perlner, R., Robinson, A., & Smith-Tone, D. (2022). Status Report on the Third Round of the NIST Post-Quantum Cryptography Standardization Process. https://doi.org/10.6028/nist.ir.8413-upd1

5. Banerjee, A., Reddy, K. T., Schoinianakis, D., & Hollebeek, T. (n.d.). PQUIP IETF 117. In Internet Engineering Task Force. Internet Engineering Task Force. Retrieved February 12, 2026, from https://datatracker.ietf.org/meeting/117/materials/slides-117-pquip-post-quantum-cryptography-for-engineers-01.

The Post-Quantum Weekly Roundup prepares technologists for the quantum computing revolution and post-quantum world.

After careful reflection, I don’t want this weekly newsletter to be only a list of links. It will now include what I do best—explanations of concepts in an intuitive, practical way. It features a Definition of the Week section, where I explain a valuable term in quantum computing and information science. This edition also includes an Academic Paper of the Week, though I’m not quite sure how it will evolve. Explaining an academic paper in a paragraph may not do it justice, and anything more than an abstract deserves its own separate article.

Definition of the Week

A Cryptographically Relevant Quantum Computer (CRQC) is a quantum computer capable of breaking widely used public-key encryption at scale. The release is predicted to be between mid-2030 and 2040.

This term, though old, appeared in a short blog post published by Google this week, calling on businesses and policymakers to prepare for when quantum computers are productized, cost-effective, and practical enough for widespread use, or for the release of a CRQC.

Academic Paper of the Week

Kim, H., Jang, K., Wang, S., Baksi, A., Song, G., Seo, H., & Chattopadhyay, A. (2026). New quantum circuits for ECDLP: Breaking prime elliptic curve cryptography in minutes (IACR ePrint Archive, Report 2026/106). https://eprint.iacr.org/2026/106

New research shows that elliptic curve cryptography, the main cryptographic scheme that powers mobile phones, blockchains, SSL/TLS web certificates, and more, can be broken in either 34 minutes with 19.1 million qubits or 96 minutes with 6.9 million qubits, using optimization strategies.

However, the paper is theoretical because the largest quantum computer has 6,100 qubits, whereas no one currently has 6.9 million qubits.

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Education

• 50 teams of Qiskit advocates (think of them as ambassadors to the Qiskit programming language) presented quantum computing projects that they’ve worked on through the Qiskit Advocate Mentorship Program. Most of the projects are quite theoretical or academic, but they all offer an overview of the academic pitch and solution, which might be useful. Watch the replay.

• Every Wednesday, the Unitary Foundation invites an academic to give a virtual talk on their recent research in quantum mechanics and/or computing. Join Quantum Wednesdays via their Discord. This week’s Quantum Wednesday is still being decided, but previous weeks included topics such as applications of quantum algorithms and quantum error correction (which addresses the many errors that occur in quantum computing).

• Practical Introduction to Quantum-Safe Cryptography, a free online course by IBM

News

• India has broken ground on its “Quantum Valley” in Amaravati, Andhra Pradesh, 1000km east of Mumbai. It will host India’s first 133-qubit quantum computer.

P.S. Here’s a photo of me at my cousin’s wedding this week in Jaipur, Rajasthan, a popular wedding destination in India. I also attended another family wedding in Mumbai and visited a friend in Pune. It’s my third time visiting the country, and maybe during my fourth, I should do a quantum computing and tech tour!

• Quantum Computing Inc. acquires Luminar Semiconductor, an advanced semiconductor fabrication company, for $110 million.

  • Large-scale quantum computer manufacturing requires expertise in semiconductor fabrication, so expect more QC companies to partner with and acquire semiconductor companies.

• Silicon Quantum Computing released a 15,000-qubit quantum simulator.

  • A quantum simulator allows you to use a cheaper classical computer (mix of CPUs and GPUs) to run quantum circuits as if they were being run on a quantum computer. You might wonder, why do we need quantum computers at all when CPUs and GPUs, which are cheaper and more accessible, can simulate them? One of my upcoming articles will explain how a quantum simulator works; quantum simulators are helpful for starting quantum projects, but they’re not quite as powerful (in other words, it’s complicated).

• UT-Austin professor Scott Aaronson, one of the most renowned academics in quantum computing and a Coinbase advisor, joins StarkWare as an advisor. StarkWare develops scaling solutions based on “STARKS,” which are advanced cryptographic proofs that handle transactions off-chain and verify them on-chain with a single, highly secure proof.

• A draft executive order aims to accelerate U.S. national quantum initiatives. Within 180 days of signing, national agencies will need to work together to develop a national quantum strategy in the United States.

• The University of Calgary revised a conversation on how the quantum internet will need satellites in space.

  • I wrote in a previous note that you cannot launch a quantum computer into space itself, as the harsh physical conditions would damage it, and that is still true. However, creating a “quantum internet” or a protocol system that connects quantum computers alongside our everyday Internet is interesting. At a high level, existing fiber-optic cables that form the current Internet destroy photons that store quantum information, making data transfer between quantum computers impossible. In contrast, new space-based cables could preserve these photons, enabling quantum computers to communicate with one another.

Technical

• The Ethereum Foundation, a major contributor to Ethereum, the second most popular blockchain, is hosting bi-weekly calls to discuss integrating post-quantum cryptography. You can find the call links and notes under “Post Quantum transaction signature (PQTS) Breakout” titles on the Ethereum Project Management Github Issues page, such as the next meeting on Wednesday, February 18, 2026, at 10:00 EST or 15:00 UTC.

  • You can see the notes from the first call on February 4, 2026. It includes a bunch of notes and comments, but here’s what I have been able to gather:

    • They widely discussed cryptographic agility, which is the ability to swap out signature algorithms without breaking all existing blockchain infrastructure.

    • They also suggested releasing the proposed improvement EIP-8141, Frame Transaction. Currently, Ethereum requires a non-quantum-resistant ECDSA signature to validate that a transaction originates from a specific user (for example, Bob sending 0.5 ETH to Alice requires a corresponding ECDSA signature proving that Bob authorized it). This new update would allow any signature scheme, including post-quantum cryptography signature schemes, to validate a transaction.

    • Since the Ethereum Foundation announced its post-quantum strategy, there’s been a wide range of suggested Ethereum Improvement Proposals (EIPs) and technical architectures that many outside of the research world won’t understand without further explanation. I’ll work on explaining (most) of them in a new post ASAP.

      • For example, Lean Roadmap, a website launched this week to monitor R&D updates on Ethereum, mentions the post-quantum signatures research track as very specific but difficult to understand without context:

        • Post-Quantum Signature Aggregation with zkVMs - Explore minimal zero-knowledge virtual machines (zkVMs) specifically optimized for signature aggregation, including various options like Binus M3, SP1, KRU, STU, Jolt, and OpenVM.

        • In other words, Ethereum must support multiple signature schemes, not just ECDSA, and likely more than one post-quantum scheme, since a current post-quantum approach might become less quantum-resistant as advances in quantum computing continue. The Ethereum Foundation is looking into technologies that generate a single, succinct proof for an entire set of (different types of) signatures to streamline blockchain operations when multiple signature schemes are supported.

• This month’s Qiskit community call is on Monday, February 23, 2026, at 10:00 A.M. Eastern Time. Join the Qiskit Discord to listen in.

New Opportunities

• The Unitary Foundation has supported more than 100 quantum tech projects through $4k grants. Applications are accepted on a rolling basis here.

• The Quantum Design Hackathon in New York City, USA, on Friday, February 20, 2026. It features various challenges focused on creating visualizations and communication strategies to make quantum computing more understandable for all. Register ASAP.

  • It is part of a wider virtual event from February 16-27, 2026, that encourages people to contribute to the open-source quantum ecosystem through the lens of community engagement and science communication. I’ve registered for the virtual event, and you should too if you're looking to gain more exposure to marketing and education in quantum computing.

    

• Cedarcrypt, July 13-16, 2026, at American University in Beirut, Mediterraneo Campus, Cyprus, is an applied cryptography summer school and conference, which includes a post-quantum cryptography track. Travel and accommodation support available for speakers. Due: April 10, 2026.

Previously shared opportunities

Education

• QuCaMP is a free summer program for high school students in the Bay Area, California, and Albuquerque, New Mexico, USA, to learn quantum physics, computing, and math. Due: Applications open February 2 to April 3, 2026.

  • It also offers a program for high school educators to learn and teach quantum computing. Applications open on the same dates.

Fellowships

• Gil Herrera Fellowship in Quantum Information Science 2026 for Ph.D. graduates who are U.S. citizens to address national security issues using quantum information science and computing. Due: ASAP.

• The Open Quantum Initiative Undergraduate Fellowship is a paid summer research program for undergraduate students in the United States on quantum computing across various universities in the Midwest. Due: February 11, 2026.

• REU at Quantum at the University of Washington is a 10-week paid summer research program for undergraduate students who are U.S. citizens or permanent residents in quantum information science and engineering. Due: February 20, 2026

• MathQuantum at the University of Maryland is a program for high school and undergraduate students that helps solve problems in quantum information science using advanced mathematical tools. Due: February 13, 2026, for the summer program.

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Please reach out if you have any feedback, are looking for anything specific that I can help find, or want to list a specific resource in an upcoming edition.

The Post-Quantum Weekly Roundup prepares technologists for the quantum computing revolution and post-quantum world. If you would like to include anything in future roundups, please send me a direct message.

Paid subscribers will receive access to the full weekly roundups, while free subscribers will get a preview (and still need to read all of my notes for the updates). Let’s see how this evolves to become something more valuable to the community.

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Overview

This week’s roundup is free for everyone because it focuses on and features a plethora of student opportunities I don’t want to gatekeep.

The emphasis on student opportunities stems from being so inspired by the young students I met online at iQuHack, MIT’s premier quantum computing hackathon, this weekend. Almost every quantum developer I knew was participating in or sponsoring the event, so make sure that you view the workshop videos and challenges. Hope that you solved the challenge or at least created something cool this weekend. I had more personal commitments this weekend than anticipated, so instead of programming a circuit, I created a website to explore the raw materials that are used to manufacture a quantum computer.

Note: 🇮🇳 I’m in India to attend a cousin’s wedding, so I haven’t had the time to focus on the latest academic research. Research resumes next week, though!

Education

• Talk videos from the Qiskit Developer Conference 2025, a premier quantum programming and developer conference, are now available on YouTube.

• If you missed iQuHack 2026, MIT’s premier quantum computing hackathon, you can still view the following hackathon challenges and workshop videos:

  • Challenges

    • Superquantum

    • Bluequbit

    • ionQ

    • NVIDIA

  • Workshops

    • Hackathon Introduction

    • ionQ, Superquantum, Bluequbit

    • NVIDIA, QuEra, IBM

    • State Street/Classiq, Alice & Bob, Quantum Rings

    • Awards and Closing Ceremony

• The MIT Quantum Winter School 2026 is a program that educates undergraduate students in the Boston, United States area on quantum computing. Course materials are publicly available.

News

• Academia Sinica, based in Taiwan, unveiled a 20-qubit quantum computer.

• IBM Research developed an algorithm that can solve non-linear, unpredictable differential equations that classical computers struggle with.

• IBM Research also outlined how using classical computers (CPUs, GPUs, ASICs, FRGAs) alongside quantum computers (QPUs) is much more valuable.

• NVIDIA is pushing for the National Quantum Initiative (NQI) Reauthorization Act to pass, which renews the 2018 act and opens major U.S. federal funding for quantum computing.

• Anduril, Davidson Technologies, and D-Wave collaborated on a missile simulation demonstrating that quantum computing can improve interception speeds by 9 to 12 percent and increase the number of intercepted missiles by 45 to 60 in a simulated attack involving 500 missiles.

• Florida Atlantic University recently placed a $20-million order with D-Wave for a quantum computer and will become the first university in the State of Florida, United States, to own one.

Technical

• Cloudflare recently published a technical article on how to create a serverless Matrix homeserver that protects all TLS connections from quantum attacks. The Matrix protocol is an open, decentralized standard for real-time messaging, voice communication, and data synchronization.

• If you have proven that a use case was more efficient to solve on a quantum computer than on a classical one, submit it to the Quantum Advantage Tracker.

• Quantum programming is now available using C++ via Qiskit: https://github.com/Qiskit/qiskit-cpp.

• This month’s Qiskit community call is on Monday, February 23, 2026, at 10:00 A.M. Eastern Time. Join the Qiskit Discord to listen in.

Opportunities

• Check out your local universities’ quantum computing program or club, as it’s the most cost-effective (often free) way to attend quantum computing lectures.

  • For example, the QuantumX program at the University of Washington, Seattle, hosts free weekly public lectures on quantum computing.

  • The Nordic Institute for Theoretical Physics also hosts free and paid workshops, lectures, and events across Scandinavia.

• The U.S. Department of Energy is seeking project proposals to conduct research using IBM’s superconducting quantum processors available through the IBM Quantum Innovation Center. Accepted proposals will get access to IBM QPUs through their very, very expensive Premium plan. Due: March 20, 2026

• IEEE Quantum Computing Week in September 2026, Toronto, Canada, has opened workshop, proposal, and technical talk proposals, as well as graduate student volunteer applications. Due: early March 2026.

Education

• QuCaMP is a free summer program for high school students in the Bay Area, California, and Albuquerque, New Mexico, USA, to learn quantum physics, computing, and math. Due: Applications open February 2 to April 3, 2026.

  • It also offers a program for high school educators to learn and teach quantum computing. Applications open on the same dates.

Hackathons

• Quantathon 3.0 for any undergraduate students who can travel for the offline portion at SRM Institute of Science and Technology (SRMIST), Kattankulathur, Chennai, India. Due: Register by February 5 and submit a PowerPoint outlining your idea by February 6.

• Quantum Days 2026 in Victoria, British Columbia, Canada. February 18-20, 2026. Due: Registration by February 4, 2026. Ticket prices are $595 for professionals and $295 for students, which are average for large quantum computing conferences.

• The 14th Annual International Hackathon for Social Good will be held from April 24 to 26, 2026, for undergraduate or graduate students. This year’s focus is quantum computing. Due: Academic faculty must nominate students for participation by February 1, 2026.

• BlueQubit’s Quantum Advantage Challenge is designed to test whether regular computers can beat quantum computers. Crack a real Bitcoin wallet containing 0.25 BTC locked behind a series of peaked-circuit puzzles. Due: ongoing

Fellowships

• Junior research fellowship at the IIT, Kharagpur, India, for a Master’s in Electrical Engineering, Computer Science, Physics, or a related field to work on reconfigurable and scalable photonic qubit architecture for quantum computing. Due: February 6, 2026

• Gil Herrera Fellowship in Quantum Information Science 2026 for Ph.D. graduates who are U.S. citizens to address national security issues using quantum information science and computing. Due: ASAP.

• The Open Quantum Initiative Undergraduate Fellowship is a paid summer research program for undergraduate students in the United States on quantum computing across various universities in the Midwest. Due: February 11, 2026.

• REU at Quantum at the University of Washington is a 10-week paid summer research program for undergraduate students who are U.S. citizens or permanent residents in quantum information science and engineering. Due: February 20, 2026

• MathQuantum at the University of Maryland is a program for high school and undergraduate students that helps solve problems in quantum information science using advanced mathematical tools. Due: February 13, 2026, for the summer program

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Please reach out if you have any feedback, are looking for anything specific that I can help find, or want to list a specific resource in an upcoming edition.

I vibe coded, or in other words, used AI (Claude Code), to create a website that shows and explains the components of a quantum computer (including the entire quantum computing system: quantum chip, quantum processing unit, and dilution refrigerator). I was inspired to build it after this week’s all-time-high metal prices, looming tariff talks, and geopolitical conflicts, as quantum computers, like all electronics, rely heavily on imported metals to carry electric current.

You can try out the web application at https://quantum-materials.vercel.app/.

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Purpose

The app should be able to answer the following questions:

1. What are the materials that make up a quantum computer? Each section of the system?

2. What materials are used for each component and use function?

3. How much do the cumulative raw materials cost?

4. Where are the raw materials most likely to come from?

Features

The features of the application include:

• The overall raw materials cost (Note: The raw materials cost is a tiny fraction of the overall cost of a quantum computer, which accounts for labor costs in engineering, R&D, and manufacturing).

• An interactive diagram listing the materials of each component of the dilution refrigerator that maintains the quantum processing unit (GPU) at its desired temperature, and the actual quantum chip

• A ranking of the material composition of a quantum computer and the breakdown of materials by type of component (category)

• A materials database that details each raw material, its percentage in the entire system, and shows the top countries supplying the raw material when hovered over.

What’s Next

Please let me know if you want me to add any other features. Other interesting features I would like to add are:

• Tariff tracker for each material

• Top companies that supply each material to top quantum computing companies

• News section on material science breakthroughs in quantum computing

I reached out to a few quantum computing companies to learn how to buy a quantum computer and to get details on their procurement of raw materials and manufacturing. I assume it will take them some time to get back to me, if they do, so I expect it will be a longer feature.

Note: The final code and sources are only for paid subscribers.

Read more

I’ve been told I share interesting updates on quantum computing, but instead of scrolling through each note, I should also compile and publish a weekly roundup.

Paid subscribers will receive access to the full weekly roundups, while free subscribers will get a preview (and still need to read all of my notes for the updates). Let’s see how this evolves to become something more valuable to the community.

The Post-Quantum Weekly Roundup prepares technologists for the quantum computing revolution and post-quantum world. If you would like to include anything in future roundups, please send me a direct message.

Overview

This week, post-quantum cryptography has become mainstream. Major cryptocurrency entities announced post-quantum cryptography strategies to protect their blockchains and blockchain-interacting apps from the security threats of quantum computing.

• Coinbase (2nd most popular cryptocurrency exchange in the world, most popular in the United States)

• Ethereum Foundation (major contributor to the Ethereum blockchain, the second most popular blockchain by transaction volume, behind Bitcoin)

• Optimism Foundation (major contributor to Optimism, a blockchain infrastructure that many other chains build on top of)

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In addition, quantum developer updates with new releases for IBM Qiskit and Microsoft Quantum Development Kit SDKs. Also, check out the upcoming hackathons and funding opportunities for your next quantum venture.

Education

• I published a primer explaining what a quantum computer actually looks like and how the low temperatures at which quantum computers must operate influence their design.

• Updated docs on BlueQubit, an easy-to-use platform to connect to the IBM Heron quantum chip and run quantum algorithms

News

• Coinbase establishes an independent advisory board for quantum computing and blockchain.

• Ethereum Foundation and Optimism Foundation announced their post-quantum cryptography strategies

• BTQ Technologies forked Bitcoin and launched a testnet named BTC Quantum that uses Dilithium signatures

• U.S. Cybersecurity and Infrastructure Security Agency (CISA) publishes a list of product categories of technologies that use post-quantum cryptography. An opportunity goldmine for anyone who wants to develop a startup for post-quantum technologies!

• Rigetti received an order from the Centre for Development of Advanced Computing (C-DAC), an Indian R&D organization under the Ministry of Electronics and Information Technology, for a 108-qubit quantum computer valued at $8.4 million.

• IonQ, a U.S.-based quantum computing company, has acquired Skywater, a U.S.-based semiconductor manufacturer specializing in silicon for quantum processors, for $1.8 billion.

• MIT is working on an efficient cooling method that can enable chip-based trapped-ion quantum computers.

Technical

• The University of Waterloo in Canada is working towards open-sourcing the first quantum computer. Check out the Open Quantum Design initiative.

• Qiskit SDK 2.0 release

  • Qiskit (Quantum Information Science Kit) is an open-source, Python-based software development kit (SDK) developed by IBM Research

• Microsoft Quantum Development Kit updates

  • Includes quantum programming with AI using GitHub Copilot

Opportunities

• Microsoft 2026 Quantum Pioneers Program seeks research proposals from academic researchers to explore the next generation of measurement-based techniques for topological quantum computing. Up to $200,000 in funding per proposal. Due: January 31, 2026

• BlueQubit’s Quantum Advantage Challenge is designed to test whether regular computers can beat quantum computers. Crack a real Bitcoin wallet containing 0.25 BTC locked behind a series of peaked-circuit puzzles. Due: ongoing

More opportunities continued:

Read more

I recently realized that “What does a quantum computer actually look like?” is often an overlooked question, especially given that quantum labs, such as the Google Quantum Lab in Santa Barbara, California, are so inaccessible that even most quantum software engineers have not visited one.

The common visualization of quantum computers isn’t exactly how they actually look in a real quantum lab. The quantum computer itself accounts for a very small part of the overall system. Its operation at very low temperatures is hardware, space, and cost-intensive, limiting its mass adoption.

This article begins by describing the temperature conditions required for a quantum computer. It then debunks the common visual representation of a quantum computer while explaining how low temperatures shape its design and hardware requirements.

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Colder temperatures than anywhere in the universe

The underlying physical environment that powers a quantum computer is highly sensitive to heat, therefore requiring storage at temperatures colder than anywhere in the universe.

A quantum computer operates at temperatures between 10 millikelvins (- 273.14 °C) and 100 millikelvins (-273.15 °C).

Other extremely cold places are warmer than a quantum computer.

The coldest place on Earth, in the East Antarctic Plateau, has a temperature of -98 °C.

The bottom of the ocean, with no access to sunlight, is between 1 °C and 2 °C.

It’s colder than all outer planets: Mercury reaches -178 °C, Uranus drops to -224 °C, and Neptune is at -214 °C. Even the coldest temperature in the outermost space is -270 °C.

Why so cold

Quantum computers operate at such low temperatures because even minor exposure to heat can cause them to lose their quantum properties.

Quantum computers are considered so powerful because they can perform multiple computations simultaneously. This is possible because they can exist in states 0 and 1 simultaneously, unlike traditional computers, which can be in only one state at a time, as noted in a previous article on qubit states.

Any heat exposure could cause a quantum computer to experience decoherence, or lose its ability to run parallel processes.

Therefore, the temperature of a quantum computer wasn’t chosen at random.

Zero Kelvin is absolute zero, the theoretical lowest possible temperature, where there is a total absence of heat. The temperature of a quantum computer ranges from 10 millikelvins (0.01 Kelvin or -273.14 °C) to 100 millikelvins (0.1 Kelvin or -273.15 °C), remaining just above absolute zero but as close as possible without the collapse of atomic motion.

Researchers are working to develop quantum computers that operate at room temperature, which is critical for mass adoption, but still face challenges.

A recent study showed that qubits began to degrade at 170 millikelvin (0.17 Kelvin, or -272.98 °C) [3].

The highest temperature at which a quantum computer still shows quantum properties is just above 1 Kelvin (-272°C), which is only slightly warmer than the warmest temperature at which quantum computers have been known to operate [2].

Debunking the common visual

A quantum computer is often visualized as a tall, cylindrical structure with golden stacked plates of decreasing size, connected by wires and rods, mounted onto a support frame, as shown in Figure 1 below.

But the cylindrical structure isn’t the “computer” that performs computation, nor is it exposed like this. Most of it is a refrigerator, and its actual design is based on the unimaginably low temperatures at which it must operate.

Quantum computer components

The components of the visual representation include the actual quantum “computer,” which comprises quantum chips and a quantum processing unit (QPU); a refrigerator to keep the quantum computer cool; and a support frame mount to allow proper thermal transfer.

The quantum chips and QPU make up the smallest part, while the refrigerator takes up most of the space.

Quantum chips

A quantum chip routes signals between qubits, the most fundamental unit of a quantum computer. It’s the size of a poststamp, or sometimes it is described as the size of an After Eight Mint square.

Google’s Willow chip contains 105 qubits. Microsoft’s Majorana 1 chip has 8 qubits, while IBM’s fleet of chip types includes Eagle with 127 qubits, Heron with 133 or 156 qubits, and Nighthawk with 120 qubits. In 2023, IBM also launched Condor, featuring over 1,000 qubits, but it no longer appears on the IBM website.

Quantum processing units (The “computer”)

Dozens of quantum chips make up a quantum processing unit (QPU). A QPU, what we often think of as a “computer,” handles computation, just as a CPU does in a classical computer. It is the size of an end table and is positioned at the narrower bottom of the stacked cylinder [5].

There is no standardized metric for evaluating quantum processing power, so it’s unclear how much compute a given QPU can handle.

Keeping the computer cold

The low temperatures required to operate an error-free quantum computer introduce hardware, physical space, and cost constraints, which are among the reasons for the slow adoption of quantum computing.

The main component, measuring two meters in length, is a commercial-grade dilution refrigerator (sometimes referred to as a cryostat) that keeps the quantum computer at frigid, unimaginably low temperatures, as shown in Figure 5 below.

The dilution refrigerator is used instead of a common food refrigerator because it can mix Helium-4 and Helium-3 atoms to become liquid helium, which is considered the coldest liquid on Earth.

The dilution refrigerator is connected to a gas-handling system that pumps in Helium atoms and a pulse tube compressor that can cool the Helium, as shown in Figure 6. The dilution refrigerator is so tall because it is a stacked system that pumps and mixes Helium atoms to produce liquid helium.

At the top of the refrigerator, the system pumps in Helium-4 and Helium-3 at room temperature (shown as Stage Name: 50K in Figure 8). Immediately below the pumps is a section of coolers (shown as Stage Name: 4K in Figure 8), followed by another section where Helium is vaporized (shown as Stage Name: 1k in Figure 8). The gas is sent to a mixing chamber, where it continues to cool, becoming liquid helium at temperatures near absolute zero. The mixing chamber with liquid helium is the coldest part of the dilution refrigerator, where the QPU, the “quantum computer,” is actually stored (shown as Stage Name: MKC in Figure 8).

The entire Helium cooling process is shown in Figure 7 below.

To maintain a low temperature, the dilution refrigerator is mounted onto a support frame to prevent vibrations from generating heat.

In a quantum lab, the entire system, including both the refrigerator and QPUs, is not exposed, as commonly depicted in Figures 1 and 5. Instead, it is covered and held within a nested, cylinder-like metal vacuum can.

So, the system in a lab does not look like the one shown in Figure 9; it is shown that way only for demo purposes.

The system will look more like Figures 10 and 11, completely covered with a metallic cylinder.

This video partially shows the assembly of a dilution refrigerator, highlighting its complexity and size, including its height, which is taller than all of the engineers assembling it:

The cost of a dilution refrigerator

Owning and maintaining a dilution refrigerator is extremely expensive.

One refrigerator costs between 300,000 and 1 million USD, with more specialized units costing more. A typical dilution refrigerator consumes 5–10 kilowatts of electrical power continuously, 24/7, amounting to about 43,800–87,600 kilowatt-hours per year, or about the yearly energy consumption of four to eight American households [1].

Low end (5 kW):
5 kW × 8,760 h = 43,800 kWh per year

High end (10 kW):
10 kW × 8,760 h = 87,600 kWh per year

Energy consumption of an American household = 10,800 kWh
43,800 kWh / 10,800 kWh = 4.0 American households
87,800 kWh / 10,800 kWh = 8.0 American households

While most quantum labs do not disclose their total number of quantum computing systems, an IBM Quantum data center near Stuttgart, Germany, began hosting two quantum computers in summer 2025 and has capacity for up to 12.

A typical quantum lab contains equipment worth hundreds of millions of dollars, which partly explains why most quantum software engineers have never been to one.

If you are interested in visiting one virtually, below is a tour video of an IBM Quantum Lab, or view the Google Quantum Lab virtual tour.

Conclusion

The low temperatures at which quantum computers must operate, and the hardware, physical space, and cost constraints required to keep them at these temperatures, are barriers to their mass adoption.

Quantum labs are very much inaccessible to the public, and even most quantum hardware engineers haven’t seen a quantum computer.

The typical visualization of a quantum computer includes many components beyond the quantum processing unit.

The QPU accounts for a very small portion of a typical visual representation of a quantum computer. Much of the structure shown is actually a dilution refrigerator that keeps the quantum computer at near-absolute zero.

Additional Sources

1. SpinQ. (2025b, May 30). Dilution Refrigerator: Everything You Need to Know [2025]. SpinQ. https://www.spinquanta.com/news-detail/the-complete-guide-to-dilution-refrigerators

2. Bhat, H. A., Khanday, F. A., Kaushik, B. K., Bashir, F., & Shah, K. A. (2022). Quantum Computing: Fundamentals, Implementations and Applications. IEEE Open Journal of Nanotechnology, 61–77. https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9783210

3. Lvov, D. S., Lemziakov, S. A., Ankerhold, E., Peltonen, J. T., & Pekola, J. P. (2025). Thermometry based on a superconducting qubit. Physical Review Applied, 23. https://journals.aps.org/prapplied/pdf/10.1103/PhysRevApplied.23.054079

4. Components of the dilution refrigerator measurement system. Bluefors. (2023, February 14). https://bluefors.com/stories/components-of-the-dilution-refrigerator-measurement-system/

5. Google. (n.d.). Discover the Quantum AI Campus. Google Quantum AI. https://quantumai.google/learn/lab

Many complexities in computer science are represented in geometric shapes and spaces. For example, vector embeddings visualize similarities in complex information, such as photos or phrases, which is critical for machine learning.

This vector embedding groups similarly handwritten numbers together, enabling machine learning-based handwriting detection:

Quantum computing is not inherently intuitive, so there are multiple geometric representations that are helpful for designing quantum algorithms. One way to represent a state of a qubit, its fundamental unit, is using the Bloch Sphere. The Bloch Sphere is a geometric model of a qubit that shows state changes as logic is applied.

You might find it helpful to read my previous article on qubit states to better understand the concepts discussed here. This part one article explains initial geometric representations in quantum computing, focusing on Bloch spheres and using as little linear algebra as possible. It analyzes different types of visual examples, both manually created and AI-generated, along with the AI prompts used to generate them.

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Why a Bloch Sphere

A Bloch sphere is spherical because the qubit state is defined by θ (theta) and φ (phi), two real, complex numbers that can be represented as a point in 3D space, such as a sphere.

One of the formulas to represent a qubit state is below, where θ (theta) and φ (phi) are included:

Within a Bloch sphere, a single vector goes in the direction to this point that represents the qubit state.

θ (theta), also known as a polar angle, is a real number between 0 and 180 degrees (also equivalent to π in trigonometry). It is the angle between the vector and the z-axis.

Another way to think of it is that θ (theta) represents the rotation from the north and south poles.

φ (phi), also known as the azimuthal angle, is a real number between 0 and 360 degrees (also equivalent to 2π in trigonometry). It is the angle of the vector on the xy plane.

Another way to think about it is that φ (phi) (azimuth) represents the rotation around the z-axis, measured in the xy plane.

Claude Opus 4.5 and Sonnet 4.5, ChatGPT 5.2, and Gemini 3 struggled with this prompt to generate a graphic similar to the one below.

Instead, Claude 4.5 accurately created an interactive Bloch sphere that lets you adjust θ (theta) and φ (phi), labelling them as polar and azimuthal angles without specifically mentioning it in the prompt. Here’s an example of the AI prompt:

Build an interactive Bloch sphere visualizer for a single qubit that renders a 3D Bloch sphere with labeled X, Y, and Z axes, shows the north and south poles as |0⟩ and |1⟩, and displays the qubit state as an arrow from the center of the sphere. The user should be able to define the state using θ and φ angles, and the visualization should update in real time as the inputs change. Include sliders for θ (0 to π) and φ (0 to 2π).

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Read more

In a recent article, I explained how to create a quantum circuit, the quantum counterpart to digital circuits that form the basis of quantum computers. Understanding the state of a quantum circuit is a crucial next step toward practical quantum applications.

Quantum state is the properties that describe a physical system, such as a qubit in a quantum computer. The unpredictability of quantum states, due to quantum mechanics, theoretically enables “unhackable” computing, as hackers cannot know outcomes without destroying the computer. However, using a quantum computer for tasks such as computation requires explicitly knowing certain parts of the state.

This article explains these complexities with as little linear algebra as possible. It outlines what a quantum state is, why it is crucial, and how to write and determine it.

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What is quantum state

Quantum state is the mathematical description, or individual properties, that describe a quantum system, or a physical system in the quantum world.

Quantum systems can be any connected part that exists in the quantum world, from an electron to lasers to a qubit that is part of a larger quantum computer.

A quantum state for an electron includes mass and velocity (kinetic energy), spin, and momentum. A quantum state for a laser consists of a coherent state (similar to light), as well as position and momentum.

A classical bit, the fundamental unit of an everyday classical computer, represents its classical state as 0 (off) and 1 (on). Bitstrings, the combination of classical bits, can represent data or instructions for processing on an everyday computer.

Quantum state for quantum computers

The field of quantum information, or using quantum states to store and process data and perform computations, is still emerging.

Like in classical computing, the quantum state of a qubit technically also enables data storage and processing. We will elaborate on the qubit state in the next section, but one common way to represent a qubit state is |0> (ket 0) and |1> (ket 1).

Some explanations describe that the state values represent charge configurations, similar to dynamic RAM, which stores data as electrical charges. Another explains them as photons being at one location or another, or both [1].

The most common explanation is that the common states are regarded as computational basis states.

Computational basis states specify the initial configuration or reference points of a qubit’s physical system, similar to a coordinate system [2].

This sphere-like visualization, called a Bloch Sphere, is more commonly used in academia and research to demonstrate the “coordinate system” of a qubit, with the computational basis states at its north and south poles labeled |0> and |1>.

Another way to think of this coordinate system is that the computational basis states form the vector space for a two-dimensional vector, with the horizontal axis corresponding to |0> and the vertical axis to |1>, as shown here.

The coordinate system would display a vector pointing along the |0> axis if the state is |0>, and along the |1> axis if the state is |1>, as shown below.

The area between the horizontal axis corresponding to the |0> direction and the vertical axis corresponding to the |1> direction is where a vector would lie if the qubit is both |0> and |1> or at a superposition.

For example, this vector graph shows the qubit state as a superposition of 0 and 1, with the vector positioned between the axes. The graph shows a 36% (0.6²) probability for state zero and a 64% (0.8²) probability for state 1. We will discuss the likelihood of the states' means in the next section.

Computational basis states for multiple qubits

The number of computational basis states in a multi-qubit circuit or system is 2^qubits, or two to the number of qubits.

A two-qubit system would have 2², or 4, computational basis states, since qubits combine all their possible individual computational basis states.

Each qubit has two computational basis states, |0> and |1>. Therefore, a two-qubit system would have |0>, |0>, |1>, and |1> as its computational basis states across the two qubits. Combining them would yield the result of |00>, |01>, |10>, and |11>.

A three-qubit system would have 2³, or 8, computational basis states, and a four-qubit system has 2^4, or 16, and so forth.

A Q-sphere is used to visualize the computational basis states of multiple qubits, rather than a Bloch Sphere, which represents only one qubit.

Determining qubit state

Computational basis states provide the foundation for describing a qubit state, but additional essential details are needed to fully understand it. The unique characteristics of quantum states are what make quantum computing so computationally powerful and secure.

The state of a qubit can be 0, 1, or a superposition of both.

The main difference is that classical states are definite and deterministic, whereas quantum states are uncertain, known only probabilistically.

When we say that the state of a qubit is |0> (ket zero), we mean that the state is fully zero. |1> (ket one) means that the state is fully one.

The mathematical rule for qubits is that the sum of the squares of amplitudes, represented as (α) alpha and (β) beta, must equal one, as shown in this formula (also known as the Born rule). The probability of zero occurring is alpha squared, while one occurring is beta squared.

Therefore, |0> or ket zero really means that the probability of zero is 100% while the probability of one is 0% as shown in the formula below. Alpha, the probability corresponding to state zero, is 100% and beta, the probability corresponding to state one, is 0%.

|1> or ket one means that the probability of zero is 0% while the probability of one is 100% as shown in the formula below. Alpha, the probability corresponding to state zero, is 0% and beta, the probability corresponding to state one, is 100%.

Another way to write a qubit state is as a column vector, with the probability of 0 at the top and the probability of 1 at the bottom. Below shows the ket zero and ket one written as column vectors.

An example with no definite probability for the states one and zero, or when the qubit is in superposition, better illustrates the mathematical rule. The vector graph shown earlier represents a superposition of 0 and 1, with 36% (0.6²) probability for state 0 and 64% (0.8²) for state 1.

The formula is then written as this:

However, what it actually means is that the probability of zero is 0.6² and the likelihood of one is 0.8². 0.6² plus 0.8² equals 1.

Its ket notation is written as 0.6 |0> + 0.8 |1>. In such a case, the qubit state can be displayed as a column vector like this:

Significance of state

The unique characteristics of qubit states make quantum computing ideal for high-performance computation and use cases requiring high security.

Unlike a classical bit, an actively used qubit (for computing) must be in a superposition of 0 and 1. This superposition allows qubits to run multiple computations simultaneously, making quantum computing extremely powerful.

An unused qubit is always in the state |0> or |1>. A qubit is |0> when it is “off” or at the ground state, or |1> when it is initialized, but no logic is applied.

Another time the qubit state is |0> or |1> is when the qubit is measured. This characteristic makes qubits extremely valuable for security applications and cryptography. When qubits are in use, they are in superposition, but as soon as the state is observed (i.e., a hacker views a password), it collapses to a definite |0> or |1>, allowing the sender and receiver to know precisely when the qubit state has been read and potentially hacked.

Over time, though, researchers will need to overcome the transmission of an unknown quantum state to build a quantum internet or a network of quantum computers that can share computing resources and handle even more powerful computing tasks.

Conclusion

Quantum state is the properties that describe a physical system in the quantum world.

In quantum computing, researchers describe the qubit state in various ways, but the most common is to view the computational basis states as defining the qubit’s vector space, much like a coordinate system.

Qubits have unique state characteristics compared to classical bits that make them ideal for future practical uses, including communication, networking, and cryptography.

Unlike classical bits, which are either 0 or 1, the state of qubits can be 0, 1, or both. This superposition allows a qubit to handle multiple computations in parallel.

Active qubits must be in this superposition, or else it is known that their state has been measured.

Sources

1. Matuschak, A., & Nielsen, M. (2019, March 18). Quantum computing for the very curious. Quantum Country. https://quantum.country/qcvc#what-does-the-quantum-state-mean

2. The qubit in quantum computing. Microsoft. (n.d.). https://learn.microsoft.com/en-us/azure/quantum/concepts-the-qubit

3. Hu, B. (2025, November 17). Quantum state in a nutshell. Bodun Hu. https://www.bodunhu.com/blog/posts/quantum-state-in-a-nutshell/

4. Quantum Information. IBM Quantum Platform. (n.d.). https://quantum.cloud.ibm.com/learning/en/courses/basics-of-quantum-information/single-systems/quantum-information

5. Zhang, P., Chen, N., Shen, S., Yu, S., Wu, S., & Kumar, N. (2022). Future Quantum Communications and Networking. IEEE Network Magazine. https://opus.lib.uts.edu.au/bitstream/10453/165421/3/Future%20Quantum%20Communications%20and%20Networking%20A%20Review%20and%20Vision.pdf