Recent works have investigated the emergence of a new kind of random matrix behaviour in unitary dynamics following a quantum quench. Starting from a time-evolved state, an ensemble of pure states supported on a small subsystem can be generated by performing projective measurements on the remainder of the system, leading to a $\textit{projected ensemble}$. In chaotic quantum systems it was conjectured that such projected ensembles become indistinguishable from the uniform Haar-random ensemble and lead to a $\textit{quantum state design}$. Exact results were recently presented by Ho and Choi [Phys. Rev. Lett. 128, 060601 (2022)] for the kicked Ising model at the self-dual point. We provide an alternative construction that can be extended to general chaotic dual-unitary circuits with solvable initial states and measurements, highlighting the role of the underlying dual-unitarity and further showing how dual-unitary circuit models exhibit both exact solvability and random matrix behaviour. Building on results from biunitary connections, we show how complex Hadamard matrices and unitary error bases both lead to solvable measurement schemes.

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双单位电路动力学中的新兴量子态设计和二单位性

最近的工作研究了量子猝灭后单一动力学中一种新的随机矩阵行为的出现。从时间演化状态开始，可以通过对系统的其余部分执行投影测量来生成一个小子系统支持的纯状态集合，从而产生 $\textit{projected ensemble}$。在混沌量子系统中，推测这种投影系综与均匀 Haar 随机系综无法区分，并导致 $\textit{量子态设计}$。Ho 和 Choi [Phys.] 最近提出了确切的结果。牧师莱特。128, 060601 (2022)] 用于自对偶点的踢伊辛模型。我们提供了一种替代结构，可以扩展到具有可解初始状态和测量的一般混沌双单位电路，强调了潜在的双重统一性的作用，并进一步展示了双重统一性电路模型如何表现出精确的可解性和随机矩阵行为。基于二元连接的结果，我们展示了复杂的 Hadamard 矩阵和酉误差基如何导致可解的测量方案。