双幺正电路中的有限浴投影系综
Finite-bath projected ensembles in dual-unitary circuits
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中文总结 AI 辅助
本研究针对双幺正电路投影系综，在有限浴尺寸下证明多项式大小的浴足以形成近似k-设计，并发展了微观输运解释，与量子游走理论建立联系。
中文摘要 AI 辅助
我们研究了由双幺正电路生成的投影系综中的涌现随机性。具体而言，我们考虑可解的双幺正砖墙电路的演化，随后对系统的一部分进行测量，从而在未测量子系统中诱导出一个态系综。先前的工作已确立，在浴尺寸较大的极限下，该投影态系综形成量子态设计，但有限浴尺寸下的收敛速率尚未被严格确立。在三个逆多项式假设下——局部置换混合、对回返运动的界限以及测量边界处的收缩——我们填补了这一空白，并证明了多项式大小的浴足以形成近似的$k$-设计。在建立我们的结果的过程中，我们发展了投影系综中涌现随机性的微观输运解释，其中偏离局部置换算子的部分表现为缺陷，并与量子游走理论建立了联系。
英文摘要
We study the emergent randomness in projected ensembles generated by dual-unitary circuits. Specifically, we consider evolution by solvable dual-unitary brickwork circuits followed by measurements on part of the system, which induce an ensemble of states on the unmeasured subsystem. Previous work has established that this projected ensemble of states forms a quantum state design in the limit where the bath size is large, but the rate of convergence at finite bath size has not been rigorously established. Under three inverse-polynomial assumptions, local permutation mixing, a bound on recurrent backward motion, and contraction at the measured boundary, we fill this gap and prove that a bath of polynomial size suffices to form approximate $k$-designs. In establishing our results, we develop a microscopic transport interpretation of emergent randomness in the projected ensemble, in which deviations from local permutation operators appear as defects, and make connections with the theory of quantum walks.
