标题： 经典欺骗系统线性交叉熵得分基准测试 显示英文标题

标题： Classically Spoofing System Linear Cross Entropy Score Benchmarking

摘要： 近年来，多个实验小组声称实现了“量子霸权”或计算量子优势。谷歌量子人工智能团队的一个重要首次声明围绕着一个称为线性交叉熵基准（Linear XEB）的指标，该指标自那时以来已被多次用于量子霸权实验。然而，由于其依赖于亚线性深度电路被证明是错误的交叉熵量子阈值（XQUATH）假设，因此伪造Linear XEB的复杂理论难度一直受到质疑。在通过量子哈密顿模拟展示量子霸权的努力中，一种类似的基准指标称为系统线性交叉熵评分（sXES），由于其与Linear XEB的根本区别，在上述负面结果的情况下仍然有效。此外，伪造sXES的复杂理论难度基于系统线性交叉熵量子阈值假设（sXQUATH），而它与XQUATH的正式关系尚不清楚。尽管sXES为未来展示量子霸权提供了承诺，但在本工作中，我们表明它是一个不合理的基准指标。特别是，我们证明sXQUATH不适用于亚线性深度电路，并提出了一种经典算法，可以伪造具有超过一定阈值噪声的实验的sXES。 显示英文摘要

摘要： In recent years, several experimental groups have claimed demonstrations of ``quantum supremacy'' or computational quantum advantage. A notable first claim by Google Quantum AI revolves around a metric called the Linear Cross Entropy Benchmarking (Linear XEB), which has been used in multiple quantum supremacy experiments since. The complexity-theoretic hardness of spoofing Linear XEB has nevertheless been doubtful due to its dependence on the Cross-Entropy Quantum Threshold (XQUATH) conjecture put forth by Aaronson and Gunn, which has been disproven for sublinear depth circuits. In efforts on demonstrating quantum supremacy by quantum Hamiltonian simulation, a similar benchmarking metric called the System Linear Cross Entropy Score (sXES) holds firm in light of the aforementioned negative result due to its fundamental distinction with Linear XEB. Moreover, the hardness of spoofing sXES complexity-theoretically rests on the System Linear Cross-Entropy Quantum Threshold Assumption (sXQUATH), the formal relationship of which to XQUATH is unclear. Despite the promises that sXES offers for future demonstration of quantum supremacy, in this work we show that it is an unsound benchmarking metric. Particularly, we prove that sXQUATH does not hold for sublinear depth circuits and present a classical algorithm that spoofs sXES for experiments corrupted with noise larger than certain threshold.