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arxiv: 2210.08556 · v2 · submitted 2022-10-16 · ❄️ cond-mat.quant-gas · quant-ph

Quantifying Quantum Computational Advantage on a Processor of Ultracold Atoms

Yong-Guang Zheng , Ying-Chao Shen , Wei-Yong Zhang , An Luo , Ying Liu , Ming-Gen He , Hao-Ran Zhang , Wan Lin
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Han-Yi Wang Zi-Hang Zhu Pei-Yue Qiu Tian-Yi Wang Ming-Cheng Chen Chao-Yang Lu Supanut Thanasilp Dimitris G. Angelakis Zhen-Sheng Yuan Jian-Wei Pan
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Pith reviewed 2026-05-24 11:08 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas quant-ph
keywords Bose-Hubbard modelquantum computational advantageultracold atomsmany-body thermalizationFloquet dynamicsquantum gas microscopesampling taskentanglement entropy
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The pith

An ultracold atom processor samples driven thermalized Bose-Hubbard states from a 10^19-dimensional Hilbert space, outpacing classical supercomputers by three orders of magnitude in sampling rate.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper seeks to establish that sampling the driven thermalized many-body states of a Bose-Hubbard system is classically intractable due to its connection with a random matrix ensemble. The authors use a quantum gas microscope with bichromatic superlattices to perform this sampling on Hubbard chains and two-leg ladders up to 64 sites with 20 atoms. They verify the thermalized phase with Bayesian tests, observe volume-law scaling of Renyi entanglement entropy, and extract multi-point correlations up to 14th order from the samples. These correlations distinguish the thermalized phase from the many-body-localized phase in regimes where tensor networks cannot deliver accurate results in reasonable time.

Core claim

Leveraging dedicated precise manipulations and atom-number-resolved detection, the experiment performs sampling of the driven Hubbard chains and two-leg ladders in the thermalized phase involving up to 64 sites with 20 atoms, yielding a Hilbert space dimension of 10^19 and outpacing the most powerful supercomputer in terms of sampling rate by three orders of magnitude. The volume law scaling of the Renyi entanglement entropy in the thermalized phase is observed. Bayesian tests verify operation in the driven thermalized phase, and multi-point correlations of up to 14th-order extracted from the experimental samples offer clear distinctions between the thermalized and many-body-localized phases

What carries the argument

The driven thermalized phase of the Bose-Hubbard system, whose sampling task becomes classically intractable through its connection to a random matrix ensemble.

If this is right

  • Volume law scaling of the Renyi entanglement entropy hinders efficient classical simulation for large systems.
  • Multi-point correlations of up to 14th order extracted from the samples distinguish the thermalized and many-body-localized phases.
  • Classical computations such as tensor networks fail to give accurate and faithful predictions within a reasonable time cost.
  • The sampling task outpaces the most powerful supercomputer by three orders of magnitude in rate.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Processors of this type could enable simulation of Floquet dynamics in other interacting chaotic systems where classical methods currently fail.
  • Extraction of high-order correlations from samples may provide a practical experimental route to phase identification beyond what low-order observables reveal.
  • Further increases in system size would likely widen the performance gap with classical sampling methods.

Load-bearing premise

The experimental system operates in the driven thermalized phase and that this phase connection to random matrix ensembles makes the sampling task classically intractable at the reported sizes.

What would settle it

A classical algorithm that samples the output strings of the driven thermalized Bose-Hubbard model at comparable speed and fidelity for 64-site, 20-atom systems, or experimental output that fails the Bayesian test for the thermalized phase.

Figures

Figures reproduced from arXiv: 2210.08556 by An Luo, Chao-Yang Lu, Dimitris G. Angelakis, Han-Yi Wang, Hao-Ran Zhang, Jian-Wei Pan, Ming-Cheng Chen, Ming-Gen He, Pei-Yue Qiu, Supanut Thanasilp, Tian-Yi Wang, Wan Lin, Wei-Yong Zhang, Ying-Chao Shen, Ying Liu, Yong-Guang Zheng, Zhen-Sheng Yuan, Zi-Hang Zhu.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
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Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
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Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

Nonequilibrium dynamics of quantum many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analogue quantum simulators. Owing to the intimate connection with a random matrix ensemble, it is proposed to be classically intractable to sample the driven thermalized many-body states of a Bose-Hubbard system, and further extract multi-point correlations from the output-strings for characterizing quantum systems. Here, leveraging dedicated precise manipulations and atom-number-resolved detection through a quantum gas microscope with bichromatic superlattices, we perform sampling of the driven Hubbard chains and two-leg ladders in the thermalized phase involving up to 64 sites with 20 atoms, yielding a Hilbert space dimension of $10^{19}$ and outpacing the most powerful supercomputer in terms of sampling rate by three orders of magnitude. The volume law scaling of the \Renyi entanglement entropy in the thermalized phase is observed, which hinders efficient classical simulation for large systems. We employ the Bayesian tests to verify that our prepared systems operate in the driven thermalized phase. Multi-point correlations of up to 14th-order extracted from the experimental samples offer clear distinctions between the thermalized and many-body-localized phases, where classical computations such as tensor network fails to give accurate and faithful predictions within a reasonable time cost. Our work demonstrates the sampling of a interacting chaotic system performed on a quantum processor of ultracold atoms and opens the door of utilizable quantum computational advantage in simulating Floquet dynamics of many-body systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 0 minor

Summary. The paper reports an experimental realization of sampling driven thermalized many-body states in Bose-Hubbard chains and ladders (up to 64 sites, 20 atoms, Hilbert dimension 10^19) using a quantum gas microscope. It claims this sampling task is classically intractable owing to an intimate connection with a random-matrix ensemble, demonstrates volume-law Rényi entropy scaling, verifies the thermalized phase via Bayesian tests, extracts up to 14th-order correlations that distinguish thermalized from many-body-localized phases, and reports a three-order-of-magnitude sampling-rate advantage over the most powerful supercomputer.

Significance. If the classical intractability claim can be placed on a firmer footing, the work would constitute a notable experimental step toward practical quantum advantage in simulating interacting Floquet many-body systems. The atom-number-resolved detection, high-order correlation extraction, and direct comparison to tensor-network methods are concrete strengths. The current heuristic link to random-matrix ensembles, however, leaves the central advantage assertion open to further scrutiny.

major comments (3)
  1. [Abstract] Abstract: the claim that sampling is 'classically intractable' rests on an 'intimate connection with a random matrix ensemble' without a formal complexity reduction or explicit argument that every efficient classical sampler must fail at the reported system sizes.
  2. [Abstract] Abstract: no quantitative classical runtime benchmarks (e.g., wall-clock times or scaling for tensor-network or other methods on equivalent tasks), error bars on measured sampling rates, or data-selection criteria are supplied, preventing a precise assessment of the reported three-order-of-magnitude advantage.
  3. [Abstract] Abstract: Bayesian tests are invoked to confirm the driven thermalized phase, yet no analysis quantifies how robust the intractability claim remains under realistic decoherence, finite-size corrections, or deviations from perfect thermalization.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We appreciate the referee's insightful comments on our manuscript. We provide point-by-point responses below and outline the revisions we intend to implement to address the concerns raised.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that sampling is 'classically intractable' rests on an 'intimate connection with a random matrix ensemble' without a formal complexity reduction or explicit argument that every efficient classical sampler must fail at the reported system sizes.

    Authors: We acknowledge that our claim of classical intractability is based on a heuristic connection to random matrix theory rather than a formal complexity-theoretic reduction. In the thermalized phase, the driven Bose-Hubbard system exhibits chaotic dynamics where the Floquet eigenstates are expected to follow random matrix statistics, making exact sampling from the resulting distribution computationally prohibitive for classical methods at the reported Hilbert space dimensions. While we do not claim a rigorous proof that no efficient classical sampler exists, this heuristic is supported by the observed volume-law entanglement entropy and the failure of tensor-network methods to reproduce high-order correlations. We will revise the abstract and main text to emphasize the heuristic nature of the intractability argument and include additional references to related work on sampling complexity in chaotic quantum systems. revision: partial

  2. Referee: [Abstract] Abstract: no quantitative classical runtime benchmarks (e.g., wall-clock times or scaling for tensor-network or other methods on equivalent tasks), error bars on measured sampling rates, or data-selection criteria are supplied, preventing a precise assessment of the reported three-order-of-magnitude advantage.

    Authors: We agree that providing quantitative benchmarks would strengthen the comparison. In the revised manuscript, we will include in the supplementary information detailed wall-clock time estimates for classical methods such as tensor-network contractions on smaller systems, extrapolated scaling to the experimental sizes, error bars on the experimental sampling rates derived from multiple experimental runs, and the criteria used for data selection (e.g., atom number and fidelity thresholds). This will allow a more precise evaluation of the reported sampling advantage. revision: yes

  3. Referee: [Abstract] Abstract: Bayesian tests are invoked to confirm the driven thermalized phase, yet no analysis quantifies how robust the intractability claim remains under realistic decoherence, finite-size corrections, or deviations from perfect thermalization.

    Authors: The Bayesian tests compare the observed probability distributions and correlation functions against those expected from the thermal ensemble. To address robustness, we will add a discussion in the main text analyzing the sensitivity of the sampling task to small deviations from thermalization, including estimates of how decoherence would affect the high-order correlations and the volume-law entropy scaling. While a comprehensive numerical study of all possible deviations is beyond the scope of the current work, the experimental parameters are chosen such that the system is deep in the thermalized regime, as evidenced by the agreement with random-matrix predictions. We will clarify these points in the revision. revision: partial

Circularity Check

0 steps flagged

No circularity: advantage claim rests on external sampling-rate comparison

full rationale

The paper measures experimental sampling rates on a 64-site Bose-Hubbard system and directly contrasts them with tensor-network runtimes on classical hardware; this comparison is external and does not reduce to any fitted parameter or self-referential definition inside the manuscript. The intractability premise is introduced as an external proposal tied to random-matrix ensembles rather than derived from the paper's own equations or data, and no load-bearing step (entropy scaling, correlation extraction, or phase verification) is shown to be equivalent to its inputs by construction. Bayesian tests and volume-law observations are presented as independent empirical checks, not tautological outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the intractability premise is attributed to prior proposal rather than derived here.

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