发表机构
University of Oxford（牛津大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明在含噪声随机电路中，动力学诊断与经典可模拟性可双向分离，故此类诊断不能作为量子优势的证据。
AI 中文摘要
量子优势的主张依赖于模拟量子电路的经典难度。魔幻性、算子扰乱、反集中性以及费米子电路的非高斯性是复杂量子动力学的标准诊断指标。对于纯态，其中一些指标已被严格地与经典可模拟性联系起来。这些诊断指标在噪声下是否能可靠地追踪高效经典模拟的极限仍不清楚。在此，我们表明，在含噪声的Clifford+$T$和最近邻matchgate+SWAP电路中，动力学诊断与经典可模拟性可以双向分离。特别是，诊断指标在经典模拟变得高效后仍可保持非平凡，或在已知高效经典算法适用之前就变得平凡。我们将这种不匹配追溯到它们所探测的不同统计性质：魔幻性和扰乱依赖于Pauli谱的四阶统计量，而模拟算法主要依赖于二阶矩，局部噪声以不同速率抑制这些统计量。因此，在含噪声量子设备上测量的动力学诊断本身并不构成经典难度的证据。
英文摘要
Claims of quantum advantage rest on the classical hardness of simulating quantum circuits. Magic, operator scrambling, anticoncentration, and non-Gaussianity for fermionic circuits are standard diagnostics of complex quantum dynamics. For pure states, some of these have been rigorously connected to classical simulability. Whether these diagnostics reliably track the limits of efficient classical simulation under noise remains unclear. Here, we show that in noisy Clifford+$T$ and nearest-neighbour matchgate+SWAP circuits, dynamical diagnostics and classical simulability can separate in both directions. In particular, the diagnostics can remain nontrivial after classical simulation becomes efficient, or become trivial before known efficient classical algorithms apply. We trace this mismatch to the different statistical properties they probe: magic and scrambling depend on fourth-order statistics of the Pauli spectrum, whereas the simulation algorithms depend primarily on second-order moments, which local noise suppresses at different rates. Thus, dynamical diagnostics measured on a noisy quantum device do not by themselves constitute evidence for classical hardness.
Comments28 pages, 3 figures
