论文标题
随机局部量子动力学中量子复杂性的饱和度和复发性
Saturation and recurrence of quantum complexity in random local quantum dynamics
论文作者
论文摘要
量子复杂性是衡量大约准备给定状态或单一通道所需的最小数量的基本操作数量。最近，这个概念发现了量子计算以外的应用程序 - 研究量子多体系统的动态和广告黑洞的长期特性。在这种情况下，棕色和Susskind \ cite {BrownSussKind17}猜想，混乱的量子系统的复杂性在系统大小的及时及时呈线性增长，以最大值饱和，并保持最大复杂，直到在双重指数时间下且在双重次数下进行重复。在这项工作中，我们证明了基于（i）（i）随机局部量子电路和（ii）随机的局部汉密尔顿进化的两种混沌时间演变模型中复杂性的饱和度和复发性。我们的结果可以使人们了解混乱量子系统的长期行为，并可能阐明黑洞内部的物理。从技术角度来看，我们的结果是基于建立HAAR度量和高度近似设计之间的新定量连接，以及足够高深度的随机量子电路汇聚到近似设计。
Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing -- in studying the dynamics of quantum many-body systems and the long-time properties of AdS black holes. In this context Brown and Susskind \cite{BrownSusskind17} conjectured that the complexity of a chaotic quantum system grows linearly in time up to times exponential in the system size, saturating at a maximal value, and remaining maximally complex until undergoing recurrences at doubly-exponential times. In this work we prove the saturation and recurrence of complexity in two models of chaotic time evolutions based on (i) random local quantum circuits and (ii) stochastic local Hamiltonian evolution. Our results advance an understanding of the long-time behaviour of chaotic quantum systems and could shed light on the physics of black hole interiors. From a technical perspective our results are based on establishing new quantitative connections between the Haar measure and high-degree approximate designs, as well as the fact that random quantum circuits of sufficiently high depth converge to approximate designs.
