迈向可验证的量子优势与随机电路：在浓度中存活的观测量
Towards verifiable quantum advantage with random circuits: Observables that survive concentration
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中文总结 AI 辅助
本研究证明随机电路中OTOC的波动在浓度效应下仍存活，为可验证量子优势提供理论支持，并开发出改进的经典模拟算法。
中文摘要 AI 辅助
在当前量子硬件上展示量子优势是量子计算的核心目标，而随机量子电路支撑着许多领先方案。然而，基于采样的演示往往难以验证，而基于可观测量的方法则面临不同的挑战：浓度效应可能抑制电路实例之间的差异。最近的实验提出，在随机电路中估计时序外关联子（OTOC）作为可验证量子优势的一项有前景的任务，但电路间波动是否随系统规模增长而在浓度中存活仍悬而未决。在此，我们证明它们确实存活。对于任意固定空间维度中的广泛局部随机电路类别，我们证明了在系统尺度深度下，固定阶OTOC的逆多项式波动。在一维Haar随机砖墙电路中，我们进一步展示了宏观上许多门对这些波动有贡献，但在每一层中它们仍局限于亚线性宽度的区域。作为副产品，我们开发了一种经典算法，在一维OTOC的暴力经典模拟中首次实现了严格的改进。尽管经典硬度问题仍未解决，我们的结果排除了强浓度作为基于OTOC的可验证量子优势方案的障碍。
英文摘要
Demonstrating quantum advantage on current quantum hardware is a central goal of quantum computing, and random quantum circuits underpin many leading proposals. Yet sampling-based demonstrations are often difficult to verify, while observable-based approaches face a different challenge: concentration can suppress differences between circuit instances. Recent experiments have put forward the estimation of out-of-time-order correlators (OTOCs) in random circuits as a promising task for verifiable quantum advantage, yet whether their circuit-to-circuit fluctuations survive concentration as system size grows has remained open. Here we show that they do. For broad classes of local random circuits in any fixed spatial dimension, we prove inverse-polynomial fluctuations of fixed-order OTOCs at system-scale depths. In one-dimensional Haar-random brickwork circuits, we further show that macroscopically many gates contribute to these fluctuations, yet in each layer they remain confined to a sublinear-width region. As a byproduct, we develop a classical algorithm exhibiting the first rigorous improvement over brute-force classical simulation of OTOCs in 1D. Although classical hardness remains open, our results rule out strong concentration as an obstruction to OTOC-based proposals for verifiable quantum advantage.
发表机构
- Freie Universität Berlin（柏林自由大学）
- Google Quantum AI（谷歌量子人工智能）
- Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院量子信息与物质研究所）
机构由 AI 辅助整理，请以论文原文为准。
