发表机构
Southern University of Science and Technology; Faculty of Computility Microelectronics, Shenzhen University of Advanced Technology; Guangdong Provincial Key Laboratory of Computility Microelectronics; Pengxin Quantum Technology (Shenzhen) Co., Ltd.（南方科技大学; 深圳先进技术学院计算微电子学院; 广东省计算微电子重点实验室; 鹏心量子技术（深圳）有限公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明量子浅层电路优势的认证取决于单比特和成对相关性，提出基于不等式的测试，在容差内样本最优，并指出实验关键在43量子比特纠缠态。
AI 中文摘要
量子计算机被声称能产生普通经典计算机无法复现的样本。最尖锐的此类声称将恒定深度的量子电路（每次运行给定一个纠缠态）与浅层经典电路（由少输入门和有限随机性组成）进行比较。此前没有已知的高效测试能从经典样本本身认证这种声称。这里我们表明，这种测试必须读取的内容由经典类别的单比特和成对相关性模式决定，而非距离。该测试基于一个不等式：任何产生样本的机器，其与目标的距离不超过其错误标记的比例加上其字符串一半（标签之外的比特）偏离均匀的程度。一个在Lean~4证明辅助器中机器验证的坍缩定理，将第二项限制在每次采样器随机输入比特的单一设置中。四个自然检查被证明失败；第五个检查读取这些相同的相关性，能捕捉到它们无法达到的远离目标的构造，并且在少输入门类别上是精确的。标签测试被证明在其自身容差内（对数因子内）是样本最优的；第五个检查在受限固定残差类别上是可靠的，不仅是有效的，该类别是成对均匀采样器，其残差（字符串权重模素数）由少数种子固定，且种子共享有界。实验的约束是43量子比特纠缠资源态，保真度接近0.99，而非读出。剩下两个命名的开放问题；对第一个问题的肯定回答将把保证扩展到整个类别。
英文摘要
Quantum computers are claimed to produce samples ordinary classical computers cannot reproduce. The sharpest such claim known pits constant-depth quantum circuits, given one entangled state per run, against shallow classical circuits of few-input gates and limited randomness. No efficient test was known that certifies such a claim from classical samples alone. Here we show that what such a test must read is decided by the classical class's pattern of single-bit and pair correlations, not by a distance. The test rests on one inequality: any machine producing the samples sits no further from the target than the fraction it mislabels plus the deviation of its string half, the bits beyond the label, from uniform. A collapse theorem, machine-checked in the Lean~4 proof assistant, confines that second term, one setting of the sampler's random input bits at a time. Four natural checks provably fail; a fifth, reading those same correlations, catches a far-from-target construction they cannot reach, and is exact on the class of few-input gates. The label test is proven and sample-optimal in its own tolerance up to a logarithmic factor; the fifth check is sound, not only effective, on the bounded pinned-residue class, pairwise-uniform samplers whose residue, the string's weight modulo the prime, is pinned by few seeds and whose seed sharing is bounded. What binds an experiment is the $43$-qubit entangled resource state at fidelity near $0.99$, not the readout. What remains are two named open problems; a positive answer to the first would extend the guarantee to the full class.
