Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators have been realized in many experiments to study novel physics. In this work, we propose a quantum advantage protocol based on single-step Feynman-Kitaev verification of an analog quantum simulation, in which the verifier need only run an $O(\lambda^2)$-time classical computation, and the prover need only prepare $O(1)$ samples of a history state and perform $O(\lambda^2)$ single-qubit measurements, for a security parameter $\lambda$. We also propose a near-term feasible strategy for honest provers and discuss potential experimental realizations.

翻译：现有展示量子计算优势的方案受到多种实际限制，包括验证难度高及实验实现挑战大。与此同时，模拟量子模拟器已在众多实验中成功实现，用于研究新奇物理现象。本文提出一种基于单步Feynman-Kitaev验证的量子优势协议，该协议利用模拟量子模拟中的历史态验证方法：验证者仅需运行$O(\lambda^2)$时间的经典计算，证明者只需制备$O(1)$份历史态样本并进行$O(\lambda^2)$次单量子比特测量，其中$\lambda$为安全参数。我们还提出了适用于近期的诚实证明者实现策略，并讨论了潜在的实验可行性方案。