AI 中文总结
研究如何生成近似酉$k$设计，核心方法是引入双泡利踢（2PK）协议，单个混沌哈密顿量结合该协议可生成，通过评估框架势验证，还建立与配分函数关系并给出全息解释。
AI 中文摘要
酉设计提供了一种无需指数资源就能模拟哈尔随机性的有效方法。哈密顿量猝灭协议最近被证明可生成此类设计，但通常需要多次独立的哈密顿量猝灭，即便通过时间系综也是如此。本文表明无需哈密顿量猝灭：单个混沌哈密顿量就足以生成近似酉$k$设计。我们引入了双泡利踢（2PK）协议，即在固定哈密顿量下的酉演化中穿插两个泡利算符插入（踢）。通过评估框架势，我们证明所得系综收敛到哈尔值，表明近似酉设计的出现。我们在高斯随机矩阵系综、萨赫德夫 - 叶 - 基塔耶夫（SYK）模型以及简化自旋（玻色子）SYK模型中验证了该协议。此外，我们的协议允许对有限温度框架势进行规范定义，并建立了与配分函数的关系。我们从对偶引力图景概述了对我们协议的一种合理全息解释。
英文摘要
Unitary $k$-designs provide a resource-efficient framework for emulating Haar randomness up to the $k$-th order. Quench-based protocols have recently been shown to generate such designs, but achieving this typically requires multiple Hamiltonian realizations, even when using temporal ensembles. Here, we show that no independent Hamiltonians are required: a single chaotic Hamiltonian is sufficient to generate approximate unitary $k$-designs, even when that Hamiltonian is spatially local. We introduce a two-Pauli-kick (2PK) protocol, in which unitary evolution under a fixed Hamiltonian is interspersed with two Pauli operator insertions (kicks). We find that the resulting frame potential approaches the Haar value at long times, with deviations suppressed by the inverse Hilbert-space dimension. We verify this for single realizations of Gaussian random matrices, the Majorana and Spin Sachdev-Ye-Kitaev models, and deterministic local quantum spin chains. Remarkably, in deterministic spin systems, the 2PK protocol generates approximate unitary designs in regimes where quench-based protocols are either inapplicable or fail to converge. Furthermore, our protocol provides a finite-temperature extension of the frame potential and establishes an analytic bound in terms of the equilibrium partition function. We discuss a holographic perspective on this mechanism.
Commentsv3: Further analytic and numerical results added, texts organized, typos corrected
