Google Willow: what it has and has not shown

Google’s Willow is a 105-qubit superconducting chip, announced on 9 December 2024, and it carries three separate claims that are often blurred together. The first, a surface-code memory that improves as it grows, is the strongest: the Nature paper reports a logical error suppression factor of 2.14 per two steps of code distance and 0.143 percent error per cycle at distance 7. The second, a random circuit sampling run said to take 10^25 years classically, is an estimate nobody can check directly. The third, the October 2025 Quantum Echoes result, is the first Google claim designed to be reproducible on other machines, and so far the follow-up work supports it. What is not known is whether any of this scales to the logical gates a useful computer needs. Willow demonstrated a memory, not an operating logical qubit, and outside researchers have had almost no access to it.

How Willow came to exist

Willow follows Google’s 53-qubit Sycamore chip, the machine behind the 2019 supremacy claim: 200 seconds against an estimated 10,000 years on the fastest supercomputer. IBM answered that the circuits could be simulated in days on Summit, and later tensor-network work, such as a 60-GPU simulation with a cross-entropy score above Google’s own, sharpened the point. Scott Aaronson has described the 2019 experiment as long since superseded. Google’s response was to shift the goal from sampling speed to error correction.

Google’s launch post describes Willow as a 105-qubit chip built in the company’s new Santa Barbara fabrication facility, with T1 coherence times approaching 100 microseconds, roughly five times the previous generation. The error-correction preprint had appeared in August 2024, months before the chip received a name, and Aaronson noted at the time that the December event reported the same technical advance with additional publicity and a name. Our Google Willow system page records it under Alphabet, with an access status of internal.

Who owns it and who can use it

Willow belongs to Google Quantum AI, a unit of Alphabet. Our site lists it as internal access, and we found no offer to sell or lease it. Outside use has been limited. Quantum Computing Report reported an early-access proposal round with a 15 May 2026 deadline and notifications on 1 July 2026, aimed at projects designed specifically for Willow, with details of the circuits and observables to be measured. We did not find eligibility rules, how many projects were accepted, or whether any results have been published. For a benchmark story this matters: almost every number on Willow is measured by its builder on a machine no one else can run.

The hardware and the error-correction result

The surface-code paper reports two memories on Willow: a distance-7 code using 101 qubits and a distance-5 code with a real-time decoder. The distance-7 memory had a logical error of 0.143 percent per error-correction cycle, and the logical qubit outlived its best physical qubit by a factor of 2.4. The distance-5 run held below-threshold performance across a million cycles with an average decoder latency of 63 microseconds against a cycle time of 1.1 microseconds. Google’s post summarises this as halving the error rate each time the grid grew from 3x3 to 5x5 to 7x7.

That scaling is the point. Below threshold, adding qubits lowers the error instead of raising it, which is the precondition for any large machine. It is also a result about one operation, storing a quantum state. Aaronson’s reading is that Google defines a true fault-tolerant qubit as one running fault-tolerant two-qubit gates at about 10^-6 error, and Willow has produced a single encoded qubit without operating on it. A distance-7 patch at 0.143 percent per cycle is therefore several orders of magnitude from that mark. Our site’s system note makes the same cut: the result covers a memory, not logical gate operations.

Google has continued on the same hardware. In January 2026 it reported a hexagonal dynamic surface code on Willow, with an error improvement of 2.15 going from distance 3 to 5, matching a static circuit. The hexagonal layout was emulated by switching off couplers on Willow’s square grid, so it demonstrates the method, not a chip built for it. A Chinese group has also reported below-threshold behaviour: USTC’s Zuchongzhi 3.2 achieved a distance-7 surface code with a suppression factor of 1.40, per our benchmark table, lower than Willow’s 2.14. We read that as confirmation that the threshold can be crossed outside Google, and also as a measure of how much hardware quality separates 1.40 from 2.14.

Random circuit sampling and its estimate

Willow’s second claim is a random circuit sampling run completed in under five minutes that Google estimates would take 10^25 years on a leading supercomputer. The underlying method, cross-entropy benchmarking, had been published for the earlier chip as 67 qubits at 32 cycles, with an argument that noisy circuits settle into a computationally complex phase. A comment relayed on Aaronson’s blog puts the Willow experiment at 103 qubits at several depths, with a depth-40 cost point at a fidelity near 0.1 percent. That is a secondhand figure and we did not find it in a Google primary source.

Aaronson’s key caution is that for the same reason the task would take 10^25 years to simulate, it would take that long to verify. Google checked the score on smaller circuits, ran tensor-network contractions at intermediate sizes and extrapolated. He also calls the task one with no practical utility. The 10^25 years is therefore an extrapolated cost estimate under the best known classical algorithms and a particular memory budget, not a measurement.

Theory has since narrowed the room for such estimates. A 2025 paper by Lee and colleagues shows noisy random circuits can be sampled classically in polynomial time in one dimension and quasi-polynomial time in higher dimensions, provided conditional mutual information decays exponentially. That does not say Willow’s circuits are easy, because we have not seen an analysis showing the condition holds at its noise level. It does mean the claim depends on assumptions about noise that are an active research question. We found no published end-to-end classical reproduction of Willow’s sampling task.

Quantum Echoes: the verifiable claim

In October 2025 Google published a Nature paper, Observation of constructive interference at the edge of quantum ergodicity, and branded the method Quantum Echoes. It measures a second-order out-of-time-order correlator (OTOC): evolve a system forward, apply a small perturbation, evolve backward, and read out an interference signal. Unlike sampling, the output is an expectation value that should come out the same on any good enough machine, which is why Google calls it verifiable. Google’s announcement states a speedup of 13,000 times over the best classical algorithm on a leading supercomputer.

The details are narrower than the headline. The experiments used 103 qubits, and 65 qubits for the complexity demonstration, at roughly two hours on Willow against an estimated 3.2 years per data point on Frontier. The arXiv version lists a 103-qubit processor and credits Dmitry Abanin with 264 co-authors. According to a trade report, the two-qubit error was about 0.15 percent, signal-to-noise ratios ran 2 to 3, and extensive error mitigation was needed; we did not verify those figures against the paper. A molecular NMR experiment on 15-atom and 28-atom molecules matched conventional data, but Google’s own description says the NMR application is not yet beyond classical capability.

The classical response has so far favoured Google. An April 2026 preprint concludes that tensor networks with belief propagation, the family of methods that challenged IBM’s 2023 result, cannot feasibly simulate the experiment because the circuits generate too much entanglement. Its author list includes Google Quantum AI researchers, so it is a self-test of a credible challenger, not an independent verdict. A broader 2026 review of tensor-network methods treats the IBM, D-Wave and Google claims together and says better classical methods will raise the bar. The tracker that IBM and partners launched in February 2026, described in the IBM announcement, has shown classical methods can catch a quantum runtime within weeks, so the 13,000x figure should be treated as a claim with a date on it.

What the numbers do and do not show

A short comparison helps separate the three claims by how much they depend on an estimate.

Claim	Stated figure	What backs it	What it depends on
Below-threshold memory	2.14x per distance step, 0.143% per cycle	Measured on the chip, peer reviewed	Hardware only, no classical estimate
Random circuit sampling	10^25 years classically	Extrapolated score from smaller circuits	Best known classical algorithm and memory budget
Quantum Echoes	13,000x on a second-order OTOC	Measured signal plus estimated Frontier cost	Classical estimate of 3.2 years per data point

Only the first row can be falsified by measuring the chip alone. The other two are ratios whose denominator is a classical-cost estimate, which is why they have moved before. Rivals report similar figures on the same task type. USTC’s 105-qubit Zuchongzhi 3.0 ran sampling on 83 qubits for 32 cycles and put the classical cost at 6.4 billion years on Frontier, and Quantinuum claimed a 100-fold improvement on Google’s 2019 cross-entropy score on 56 trapped-ion qubits. Each is a vendor-stated estimate. The coherence figure is also an approximation: Google says T1 is approaching 100 microseconds, a rounded number, not a device median with an error bar, and our table records it as approximate.

The error-correction numbers also need context from the cycle time. A 1.1 microsecond cycle means a distance-5 memory ran for a million cycles in a little over a second of wall-clock time. That proves stability over many cycles but over a very short time, and long-lived logical memories of seconds or minutes are a different engineering target.

What remains unproven

Four gaps matter. First, logical operations: nothing in the sources we fetched shows Willow running error-corrected two-qubit gates, and Aaronson’s 10^-6 mark is far away. Second, scale: a distance-7 memory uses 101 of 105 qubits, so Willow cannot host a larger code or several logical qubits at once. Third, usefulness: Google says its aim is useful, beyond-classical computation for medicine and energy, and the NMR demonstration is explicitly not there yet. Fourth, independence: neither the sampling result nor the echoes result has been reproduced on a different quantum computer, and external access is limited to a selective programme.

What we could not confirm

We found no Google source on Willow’s power draw, cooling, or the cost of building and running it, so we say nothing on those. We could not retrieve Google’s roadmap page, and the milestone definitions above come from Aaronson’s account. The 103-qubit and 0.1 percent figures for the sampling experiment come from a blog comment as relayed in a summary of Aaronson’s post. The two-qubit error and signal-to-noise figures for Quantum Echoes come from a trade report. We did not read the Nature papers directly, because Nature’s pages require a login redirect; the arXiv versions and Google’s posts were used instead. We did not confirm how many early-access projects were accepted.

What to watch

Watch for a logical two-qubit gate or lattice surgery result on Willow or its successor, results from external teams in the early-access programme, a second machine reproducing the OTOC value, and any classical group showing a feasible simulation of the echoes data. A reproduction of the sampling result by classical means would not undercut the error-correction scaling, which is a separate and sturdier result. For the wider context of how these claims are scored, see our quantum benchmarks table and the quantum section.

Sources

• Google Willow launch post: https://blog.google/technology/research/google-willow-quantum-chip/
• Below-threshold surface code paper: https://arxiv.org/abs/2408.13687
• Google 2019 supremacy post: https://research.google/blog/quantum-supremacy-using-a-programmable-superconducting-processor/
• IBM response to 2019 claim: https://arxiv.org/abs/1910.09534
• Pan and Zhang Sycamore simulation: https://arxiv.org/abs/2103.03074
• Aaronson, The Google Willow thing: https://scottaaronson.blog/?p=8525
• Willow early access (QCR): https://quantumcomputingreport.com/google-quantum-ai-is-now-accepting-proposals-for-early-access-to-their-willow-quantum-processor/
• Dynamic surface codes post: https://research.google/blog/dynamic-surface-codes-open-new-avenues-for-quantum-error-correction/
• IBM Quantum Advantage Tracker: https://www.ibm.com/quantum/blog/quantum-advantage-tracker
• Zuchongzhi 3.0 sampling: https://arxiv.org/abs/2412.11924
• Quantinuum 56-qubit H2 release: https://www.prnewswire.com/news-releases/quantinuum-launches-industry-first-trapped-ion-56-qubit-quantum-computer-breaking-key-benchmark-record-302164906.html
• Zuchongzhi 3.2 distance-7 code (PRL): https://journals.aps.org/prl/abstract/10.1103/rqkg-dw31
• Phase transition in random circuit sampling: https://arxiv.org/abs/2304.11119
• Classical simulation of noisy random circuits: https://arxiv.org/abs/2510.06328
• A verifiable quantum advantage (Google Research): https://research.google/blog/a-verifiable-quantum-advantage/
• Quantum Echoes announcement: https://blog.google/innovation-and-ai/technology/research/quantum-echoes-willow-verifiable-quantum-advantage/
• OTOC arXiv paper: https://arxiv.org/abs/2506.10191
• Quantum Echoes trade report: https://thequantuminsider.com/2025/10/22/google-quantum-ai-shows-13000x-speedup-over-worlds-fastest-supercomputer-in-physics-simulation/
• TNBP cannot simulate echoes: https://arxiv.org/abs/2604.15427
• Tensor network review: https://arxiv.org/abs/2603.18825