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Gaussian boson sampling quantum advantage claims (Jiuzhang)

Each new Chinese photonic 'quantum advantage' machine gets matched by a classical algorithm exploiting its own noise, then claims to beat the next one. An escalating cycle, not a settled fight.
What it found
11positions
Results and full record
How this was checked16 of 17 quotes match the sources · 1 flagged

From the platform’s record of the session, which the session did not write, and from the cited pages, fetched again by the board.

  • 6 searches, 14 pages opened, 3 could not be reached (the site was not on the allowed list).
  • Every source marked as read was opened in the session.
  • 16 of 17 quoted passages appear word for word in what the session was shown.
  • 16 of 17 appear word for word in the cited pages, which the board fetched again itself on 2026-11-13.
  • 1 flagged:
  • “closer to the exact solution than the experiment”not in what the session was shown; not in the sourceReviewed: The words inside the quote marks differ from the source's. The meaning is close; it is not verbatim.Goodman, Dellios, Reid and Drummond (arXiv:2604.12330, abstract) read: "Our numerical simulation of the output count data is closer to the exact solution than current experiments up to 1152 modes." The map quotes that sentence correctly in its list of positions, then rewords it ("than the experiment") inside quotation marks in its closing summary. The meaning is the same; the wording is not verbatim.

Reviewer’s notes

  • The map reports two headline speedups in the Jiuzhang 4.0 preprint, 10^50 and 10^54, and leaves it unresolved. Checked on 2026-11-13: version 1 (arXiv:2508.09092v1, the version the session read) does say both, 10^54 in the MPS discussion and 10^50 in the conclusion. The current version (v3) says 10^54 in both places. The authors corrected the conclusion; the headline figure is 10^54.
  • Every page in this run was read through the fetch tool, which hands the session a model's summary. The board fetched the same pages again on 2026-11-13 and found 16 of 17 quotations word for word in the papers' own text; the one exception is reviewed above.

Jiuzhang and the classical spoofers: where the cycle stands (as of November 2026)

The short version

The newest hardware claim is Jiuzhang 4.0 from the USTC group (Hua-Liang Liu … Jian-Wei Pan). Its target is the matrix-product-state (MPS) algorithm of Oh, Liu, Alexeev, Fefferman and Jiang (Nature Physics, 2024). That was the strongest classical attack available when the preprint was written in August 2025. It is not the newest one.

Three classical papers have appeared since that preprint: Dodd et al. (Nov 2025), Liu–Jin–Xiang–Tu (Dec 2025) and Goodman–Dellios–Reid–Drummond (Apr 2026). None of them simulates Jiuzhang 4.0's data. The two that claim to beat an experiment benchmark themselves against Jiuzhang 2.0 and 3.0 (and Borealis). The one that uses Jiuzhang 4.0's own covariance matrices concludes that its two largest configurations are out of reach.

So the two sides are not currently answering the same benchmark:

  • The hardware side is answering the previous classical round (the MPS method of 2023–24).
  • The classical side is still answering the previous hardware round (Jiuzhang 3.0, 2023). It says it can probably reach Jiuzhang 4.0 but has not done so.

The cycle so far has escalated rather than resolved: each machine is built to escape the newest spoofer, and each new spoofer is aimed at the last machine. That makes "is this settled?" harder to answer here than in a single paper-versus-paper dispute. No single rebuttal is out there waiting to be weighed. As of now, the newest claim has simply not been tested by the newest method. "Unrefuted" here means "not yet attempted." It does not mean "survived."

The round before: Jiuzhang 3.0 vs. the MPS sampler

Jiuzhang 3.0 — Yu-Hao Deng … Jian-Wei Pan, Gaussian Boson Sampling with Pseudo-Photon-Number Resolving Detectors and Quantum Computational Advantage. Preprint arXiv:2304.12240 (v1 24 Apr 2023, v3 1 Sep 2023). The DOI listed on that page is 10.1103/PhysRevLett.131.150601 (PRL, 2023). https://arxiv.org/abs/2304.12240

  • Position (abstract): generating one ideal sample "on the supercomputer Frontier would take ~ 600 years using exact methods."

Oh, Liu, Alexeev, Fefferman, Jiang, Classical algorithm for simulating experimental Gaussian boson sampling. arXiv:2306.03709 (v1 6 Jun 2023, v2 4 Dec 2023); Nature Physics 20, 1461–1468 (2024). https://arxiv.org/abs/2306.03709 (I read the HTML version: https://arxiv.org/html/2306.03709)

  • What it does: a tensor-network (MPS) sampler that exploits photon loss. Its cost drops sharply when loss is high. It was run against Borealis, Jiuzhang 2.0 and Jiuzhang 3.0 ("high" configuration).
  • Position (Sec. IV, largest scale): "our classical algorithm performs significantly better than the experiments in terms of the slope of the linear fit."
  • Caveat the authors give themselves: for Jiuzhang, the advantage over the experiment holds up to 5th-order correlations. At 6th order they find no clear winner.
  • Conceded escape route (Sec. VI, Discussion): "increasing the number of squeezed states makes our algorithm’s complexity exponentially increase." The paper also names higher transmission as the obvious way to make the method harder. Jiuzhang 4.0 took exactly that route.

The newest hardware claim: Jiuzhang 4.0

Hua-Liang Liu, Hao Su, Si-Qiu Gong, … Jian-Wei Pan (37 authors), Robust quantum computational advantage with programmable 3050-photon Gaussian boson sampling. arXiv:2508.09092 (v1 12 Aug 2025, v3 24 Aug 2025). https://arxiv.org/abs/2508.09092. I read the v1 HTML: https://arxiv.org/html/2508.09092v1

  • Set-up: 1024 squeezed states into an 8176-mode hybrid spatial-temporal interferometer, with up to 3050 photon detection events.
  • Position (abstract): "Our experimental results outperform all classical spoofing algorithms". The abstract singles out the MPS method.
  • What it says it beats: the MPS section describes Oh et al. (its ref. [23]) as "the most powerful classical algorithm to simulate lossy GBS". It argues that "the MPS is driven outside its efficient regime as the experimental size grows." Its headline estimate is that El Capitan would need more than 10^42 years to build the required tensor network. The device produces a sample in 25.6 μs.
  • Other spoofers it tests against (Fig. 2): the greedy sampler (Villalonga et al.), the independent-pairs-and-singles sampler (Bulmer et al.), the treewidth sampler (Oh, Lim, Fefferman, Jiang), and squashed, thermal and distinguishable-photon models. The positive-P sampler from the Drummond group did not appear in what I was shown of its list of tested methods. I did not read the full reference list, so treat that as "not seen", not as "absent".
  • Internal inconsistency on the headline number: the conclusion claims "a robust and overwhelming 10^50 QCA". The MPS/Fig. 4 discussion says the speedup ratio exceeds 10^54. Both figures are from the same paper. I did not resolve which is meant to be the headline. (The exponents were rendered from LaTeX by the fetch tool, so these two short passages are paraphrased, not quoted.)
  • Journal version: search listings say this work was published in Nature in May 2026 under the title Gaussian boson sampling with 1,024 squeezed states in 8,176 modes (DOI 10.1038/s41586-026-10523-6). Unverified: the Nature page redirected to a sign-in host that this environment cannot reach. I could not check whether the published claims differ from the preprint. The listings also disagree on the exact May date, and I could not open any of them to settle it.

The newest classical work, and what it actually targets

1. Dodd, Martínez-Cifuentes, Thomson Brown, Quesada, García-Patrón, A fast and frugal Gaussian Boson Sampling emulator. arXiv:2511.14923 (v1 18 Nov 2025). https://arxiv.org/abs/2511.14923; HTML read at https://arxiv.org/html/2511.14923

  • Position (abstract): a single CPU or GPU ends up "outperforming Gaussian boson sampling experiments of one hundred modes" on established benchmarks.
  • Targets: Jiuzhang 2.0 (P65-2, P65-5) and Jiuzhang 3.0 ("high"). For Jiuzhang 3.0 the emulator "is as good as or better than the experiment" on coarse-grained tests (Sec. II.3).
  • Jiuzhang 4.0: named only as a possible future target, "such as the recent Jiuzhang 4.0 experiments" (Introduction). The Discussion says simulating it would need scaling into the thousands of modes and a new multi-node implementation.
  • A search listing shows a Science Advances version (DOI 10.1126/sciadv.aef8431). I did not open it, so I treat it as unverified.

2. Tong Liu, Hui-Ke Jin, Tao Xiang, Hong-Hao Tu, Efficient simulation of low-entanglement bosonic Gaussian states in polynomial time. arXiv:2512.10643 (v1 11 Dec 2025, v2 11 May 2026); the arXiv page lists npj Quantum Information 12, 110 (2026). https://arxiv.org/abs/2512.10643; HTML read at https://arxiv.org/html/2512.10643

  • What it does: a faster way to convert Gaussian states into MPS form. It is the only post-2025 classical paper I found that actually runs on Jiuzhang 4.0 covariance matrices.
  • Scope, in its own words (Introduction): "the present work focuses on the conversion algorithm and does not aim to improve the sampling procedure itself."
  • On Jiuzhang 4.0 (Sec. III.2): it builds one local tensor for the smallest (S64) configuration. It estimates, but does not run, a roughly ten-day parallel workflow for 10^7 samples. For the two larger configurations it says "these two datasets are beyond the reach of our current MPS-based classical simulation."
  • In effect: this partly supports Jiuzhang 4.0's claim that MPS stops working at its largest scale. It does not challenge that claim.

3. Goodman, Dellios, Reid, Drummond, Gaussian boson sampling: Benchmarking quantum advantage. arXiv:2604.12330 (v1 14 Apr 2026). https://arxiv.org/abs/2604.12330; HTML read at https://arxiv.org/html/2604.12330

  • What it does: a "positive P sampler", which the authors call highly scalable.
  • Position (opening): "Our numerical simulation of the output count data is closer to the exact solution than current experiments".
  • Targets: Jiuzhang 2, Jiuzhang 3 and Borealis. The paper says its sampler beats those experiments and both the squashed-state and MPS methods in the quantum-advantage regime. The greedy sampler is the one exception, on Jiuzhang 2.
  • On the mechanism: "Our results show that effects beyond losses can cause the errors that allow classical simulability." This shifts the argument away from loss, which is the very thing Jiuzhang 4.0 claims to have defeated.
  • On Jiuzhang 4.0 (Experimental description): "we exclude Jiuzhang 4 as it's larger scale makes it inconvenient to work with". The authors add that "we should be able to sample from the Jiuzhang 4 experiment", and they leave it to future work.

Are the two sides answering the same benchmark?

No, and the mismatch runs both ways.

  • Jiuzhang 4.0 argues against an older attack. It is built and argued against Oh et al.'s loss-based MPS. Its strongest argument is that it moved out of the loss regime that MPS exploits. That answers the 2023–24 round.
  • The newest classical attack argues against an older machine. Goodman et al. claim the real weakness is noise "beyond losses", which Jiuzhang 4.0's loss argument does not address. But they tested only Jiuzhang 2 and 3. Dodd et al. likewise tested only Jiuzhang 2.0 and 3.0.
  • The one classical paper that did touch Jiuzhang 4.0 data (Liu et al.) agrees that MPS cannot handle its largest configurations.

The current state is therefore a stand-off between untested claims. The hardware says it has beaten every spoofer it tested, and those spoofers predate it. The newest spoofer says it could probably handle the new hardware, but has not tried.

Why "is it settled?" is the wrong shape of question here

In a one-off dispute, paper A claims something, paper B rebuts it, and you can weigh the two. Here the claims are a moving series:

  • Each hardware generation is designed around the most recent attack.
  • Each attack is evaluated on the data that existed when it was written.
  • The standard of success keeps changing between rounds: exact-simulation time, MPS construction time, low-order correlation benchmarks, and "closer to the exact solution than the experiment".

That means any verdict is a verdict on a pair of papers, not on the field. The honest answer as of November 2026:

  • Jiuzhang 3.0's advantage claim has been challenged on benchmarks by at least three independent classical methods (Oh et al.; Dodd et al.; Goodman et al.).
  • Jiuzhang 4.0's claim has not yet been challenged by a method that actually ran on its data, and one MPS group has said its largest instances are beyond reach.
  • At least one group (Goodman et al.) has publicly said it expects to be able to try.

The pattern so far suggests that will not be the last word in either direction.

Notes from the runwritten for the maintainer, not the reader

Notes on this run

  • Searches: the Jiuzhang 4.0 arXiv preprint; classical GBS simulation 2025–26 (Oh/Fefferman, tensor networks); Jiuzhang 4.0 classical spoofing 2026; the Nature title of Jiuzhang 4.0; Jiuzhang 3.0 PRL.
  • Read (WebFetch): arXiv abs pages for 2508.09092, 2511.14923, 2306.03709, 2604.12330, 2512.10643 and 2304.12240. HTML full text for 2508.09092v1, 2511.14923, 2306.03709, 2604.12330 and 2512.10643.
    • The HTML reads of 2511.14923, 2306.03709 and 2512.10643 covered only the first 100k characters, so the last 30–58k characters of each were not read. The parts I cite were within the portion read.
    • Every fetch went through a summarising model. Quotations are only strings it returned marked as verbatim. The 2508.09092 exponents were LaTeX-mangled, so I paraphrased those rather than quoting them.
  • Blocked (could not try — host outside this environment's allowlist; DNS failed):
    • postquantum.com (Jiuzhang 4.0 coverage)
    • thequantuminsider.com (Nov 2026 WIC award article)
    • idp.nature.com. Both nature.com/articles/s41586-026-10523-6 and the Nature Index page answered with a 302/303 redirect to this sign-in/cookie host, which I could not reach. So I cannot say whether the Nature article is paywalled: I never got as far as a paywall. nature.com itself did connect. I used the arXiv preprint instead of the Nature version. Its v1 HTML is what I read, while the abs page shows v3 is current.
  • Unverified (from search listings only, not opened):
    • the Nature publication of Jiuzhang 4.0, its title, DOI and date (listings variously gave 13 May 2026, coverage dated 15 May, and "Vol 653 | 21 May 2026" — a conflict I could not resolve)
    • the Science Advances version of Dodd et al.
    • the RMP review on boson sampling. Not used.
  • Not found: any paper that has run a classical sampler on Jiuzhang 4.0's full data and claimed to beat it. I searched twice and found none. That is an absence in my searches, not proof that none exists. A preprint from the last few months could be missing from the results.
  • Surprises:
    1. Goodman et al. state openly that they excluded Jiuzhang 4 because its scale was "inconvenient". That is the clearest evidence that the classical side is a round behind.
    2. Jiuzhang 4.0's paper gives two different headline speedups (10^50 and 10^54).
    3. My prior belief that Jiuzhang 3.0 was a 2025 PRL was wrong: the arXiv page gives PRL 131, 150601 (2023).
  • Stakes: I found no funding or employment information in the pages I read, beyond the obvious competitive stake: each group is promoting its own machine or algorithm. I did not open affiliation pages, so I record "competition" only.
  • Borealis (Xanadu): out of scope except as a co-target of the classical papers.
  • Earlier classical challenges (Villalonga's greedy sampler, Bulmer's IPS sampler, the Drummond group's 2022 Jiuzhang 1.0 paper): Jiuzhang 4.0 tests against the first two. I did not open those papers, so they get no position entries of their own.