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.

翻译：近年来，多个实验团队声称实现了“量子霸权”或计算量子优势。谷歌量子人工智能团队的首个著名声明围绕一个名为线性交叉熵基准测试（Linear XEB）的指标展开，该指标此后被用于多项量子霸权实验。然而，由于欺骗Linear XEB的复杂性理论难度依赖于Aaronson和Gunn提出的交叉熵量子阈值（XQUATH）猜想（该猜想已被亚线性深度电路证伪），其可靠性一直存疑。在通过量子哈密顿模拟展示量子霸权的尝试中，类似基准测试指标——系统线性交叉熵分数（sXES）因与Linear XEB存在根本性区别，在上述负面结果中仍保持稳健。此外，sXES欺骗难度的复杂性理论上依赖于系统线性交叉熵量子阈值假设（sXQUATH），其与XQUATH的形式关系尚不明确。尽管sXES为未来量子霸权演示提供了前景，但本研究表明它并非可靠的基准测试指标。具体而言，我们证明了sXQUATH不适用于亚线性深度电路，并提出了一种经典算法，能够在噪声超过特定阈值时欺骗sXES实验。