AI 中文总结
本研究针对解码量子干涉测量（DQI），通过马尔可夫链蒙特卡罗（MCMC）方法研究经典采样算法能否模拟其优化能力，发现MCMC可在一定规模问题上匹配DQI性能，为DQI实际优势提供了更细致视角。
AI 中文摘要
优化问题是工业相关量子优势的主要候选方向之一。解码量子干涉测量（Decoded Quantum Interferometry, DQI）已被提出用于解决近似优化问题，建立了与经典解码问题的联系。尽管先前工作主要关注DQI的理论复杂性，但相对于经典算法，其经验性能的了解相对较少。本研究进一步阐明了DQI的复杂性，并通过数值研究经典采样方法是否能模拟DQI的优化能力。我们首先对DQI进行简化的分析表征，将其预期性能与二项式统计关联起来，并确定了进一步研究DQI复杂性的具体障碍。利用DQI输出概率可高效计算的特性，我们应用马尔可夫链蒙特卡罗（Markov Chain Monte Carlo, MCMC）技术，特别是块吉布斯采样，从诱导分布中采样。我们针对两个优化问题研究这些方法的运行时间缩放：max-XORSAT问题中，我们达到了超过1000个有效量子比特；OPI问题中，我们达到了超过150个有效量子比特。结果表明，在广泛的问题规模下，MCMC算法可可靠达到DQI预期的近似比率。在OPI问题中，当DQI被声称具有超多项式优势的区域，我们观察到MCMC的经验运行时间缩放近似为1.1ⁿ，即具有相对较小基数的指数增长。我们的发现并未反驳现有的量子优势主张，但提供了新的经验证据，表明经典采样算法可紧密匹配DQI的优化性能，为DQI的实际优势提供了更细致的视角。
英文摘要
Optimization problems are among the leading candidates for industrially relevant quantum advantage. Decoded quantum interferometry (DQI) has been proposed to tackle approximate optimization, establishing a connection to classical decoding problems. While previous work has primarily focused on the theoretical complexity of DQI, comparatively little is known about its empirical performance relative to classical algorithms. In this work, we shed further light on the complexity of DQI and investigate numerically whether classical sampling methods can emulate the optimization capabilities of DQI. We first present a simplified analytical characterization of DQI that connects its expected performance to binomial statistics, and we identify concrete obstacles in further studying the complexity of DQI. Exploiting the fact that DQI output probabilities are efficiently computable, we apply Markov chain Monte Carlo (MCMC) techniques, particularly block-Gibbs sampling, to sample from the induced distribution. We study the runtime scaling of these methods for two optimization problems called max-XORSAT, where we reach beyond $1000$ effective qubits; and OPI, where we reach beyond $150$ effective qubits. Our results show that MCMC algorithms can reliably attain the approximation ratios expected from DQI across a broad range of problem sizes. In OPI, in the regime where a super-polynomial advantage is claimed for DQI, we observe an empirical runtime for MCMC that scales approximately as $1.1^{n}$, indicating exponential growth with a comparatively small base. Our findings do not refute existing quantum advantage claims but provide new empirical evidence that classical sampling algorithms can closely match DQI's optimization performance, offering a more nuanced perspective on the practical advantage of DQI.
Comments24 pages (12+12), 9 figures (5+4), comments welcome
