经典可模拟量子电路与动力学的模拟成本
The cost of simulating classically tractable quantum circuits and dynamics
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中文总结 AI 辅助
本文分析经典可模拟量子电路在实践中的模拟成本，通过三种资源度量识别量子与经典模拟各自更优的区间，指出仅凭多项式可模拟性不足以决定实现方式。
中文摘要 AI 辅助
确定量子演化能否被经典高效模拟，是理解经典计算与量子计算之间界限的核心问题。然而，多项式时间可模拟性是一个渐近性陈述，其本身并不能决定（受量子启发的）经典模拟是否实际可行。事实上，不同的多项式标度可能导致截然不同的计算成本，尤其是在需要昂贵的预处理或量子数据采集时。在本工作中，我们探讨了一个问题：经典可模拟的量子动力学，在实践上是否比直接在量子硬件上执行更具资源效率。我们使用三种资源度量——量子样本数、量子时间和经典时间复杂度——对几个被广泛研究的经典可模拟电路族进行了分析。基于具有代表性的硬件级估算，我们识别出即使在存在多项式时间经典算法的情况下，量子模拟仍可能更快的参数区间，同时也识别出经典模拟仍更高效的区间。与此同时，表征未知输入态所需的大量量子采样成本，可能使得这种多项式时间经典模拟在当前基于云的硬件访问价格下变得极其昂贵。最终，我们的工作表明，仅凭多项式资源的经典可模拟性保证，不足以确定更优的实现方式。
英文摘要
Determining whether a quantum evolution can be efficiently simulated classically is central to understanding the boundary between classical and quantum computation. However, polynomial-time simulability is an asymptotic statement, and does not by itself determine whether the (quantum-inspired) classical simulation is actually practical. Indeed, different polynomial scalings can lead to vastly different computational costs, particularly when expensive preprocessing or quantum data acquisition is required. In this work, we ask whether classically simulable quantum dynamics are in practice more resource-efficient to simulate classically than to execute directly on quantum hardware. We analyze this question using three resource metrics, quantum sample, quantum time, and classical time complexity, for several widely studied classically simulable circuit families. Using representative hardware-level estimates, we identify regimes in which quantum simulation can be faster despite the existence of a polynomial-time classical algorithm, as well as regimes in which classical simulation remains more efficient. At the same time, the large quantum sampling cost needed to characterize unknown input states can make this polynomial-time classical simulation prohibitively expensive with current cloud-based hardware access prices. Ultimately, our work indicates that guarantees of classical simulability with polynomial resources alone are insufficient to determine the preferred implementation.
发表机构
- Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
- European Organization for Nuclear Research (CERN)（欧洲核子研究组织（CERN））
- Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院（EPFL））
- Chulalongkorn University（朱拉隆功大学）
机构由 AI 辅助整理，请以论文原文为准。
