探究量子动力学实验的经典复杂性

中文摘要 AI 辅助

近期一系列研究工作的汇聚表明，许多量子电路和动力学过程可以通过跟踪局部信息的经典算法高效模拟，即使传统复杂性度量（如纠缠度和魔法）很高时也是如此。在此，我们引入一种新的复杂性度量——反应性（reactivity），以捕捉这种新的经典攻击方式。与传统复杂性度量不同，反应性并非单独捕捉量子态或算符的性质，而是将量子实验作为一个整体来刻画。我们提供了数值和严格证据表明，低反应性的量子实验在众多度量下都是简单的：它们可以被经典高效模拟、学习以及快速推进。这促使我们寻找高反应性的量子实验，这些实验可能规避这些简单特征。为此，我们引入了易于实现的实验协议——称为泡利路径光谱学（Pauli path spectroscopy）——使得人们能够高效测量任何感兴趣的量子实验的反应性。我们的协议甚至在实验本身超出经典模拟能力时也适用。

英文摘要

A confluence of recent works has shown that many quantum circuits and dynamics are efficiently simulable by classical algorithms that track local information, even when conventional complexity measures such as the entanglement and magic are high. Here, we introduce a novel measure of complexity, the reactivity, to capture this new method of classical attack. Unlike conventional complexity measures, the reactivity does not capture a property of a quantum state or operator in isolation, but rather a quantum experiment as a whole. We provide numerical and rigorous evidence that quantum experiments with low reactivity are simple by a host of measures: they are efficient to classically simulate, learn, and fast-forward. This motivates the search for quantum experiments with high reactivity, which may evade these simplistic features. To this end, we introduce easily implementable experimental protocols---dubbed Pauli path spectroscopy---that allow one to efficiently measure the reactivity of any quantum experiment of interest. Our protocols are applicable even when the experiment itself is beyond the reach of classical simulation.

发表机构

• Walter Burke Institute for Theoretical Physics and Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院沃尔特·伯克理论物理研究所与量子信息物质研究所）
• Google Quantum AI（谷歌量子AI）
• PSI Center for Scientific Computing, Theory and Data and ETHZ-PSI Quantum Computing Hub, Paul Scherrer Institute（保罗谢尔研究所科学计算、理论与数据中心及ETHZ-PSI量子计算中心）

机构由 AI 辅助整理，请以论文原文为准。

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6+29 pages, 12 figures