Fastest Local Entanglement Scrambler, Multistage Thermalization, and a Non-Hermitian Phantom
Fastest Local Entanglement Scrambler, Multistage Thermalization, and a Non-Hermitian Phantom
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DOI：
10.1103/physrevx.11.031019
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发表时间：
2021-07-23
影响因子：
12.5
通讯作者：
Znidaric, Marko
中科院分区：
文献类型：
--
作者：
Bensa, Jas;Znidaric, Marko
我们研究随机量子电路及其产生二部纠缠的速率，特别是关于2-量子比特门的选择和这些应用的顺序（协议）。将该问题映射为一个马尔可夫过程，并证明了存在较大的谱等价类——不同的构型具有相同的谱。确定了以理论上可能的最快速率产生纠缠的最优门和协议。渐近热纠缠的弛豫是通过局部弛豫速率的一系列相变进行的，这是非厄米性的结果。特别是，非厄米性可能导致速率比矩阵特征值间隙预测的更快，或者更有趣的是，更慢。这个结果是由膨胀系数随着系统大小呈指数增长引起的，导致“幻影”特征值，并且是由于非厄米特征向量的非正交性。我们在数值上证明了这种现象也发生在具有非最优通用门的随机电路中，随机U(4)门，也没有空间或时间随机性，这表明它可能在其他非厄米设置中具有广泛的重要性，包括相关性。
We study random quantum circuits and their rate of producing bipartite entanglement, specifically with respect to the choice of 2-qubit gates and the order (protocol) in which these are applied. The problem is mapped to a Markovian process, and we prove that there are large spectral equivalence classes-different configurations have the same spectrum. Optimal gates and the protocol that generate entanglement with the fastest theoretically possible rate are identified. Relaxation towards the asymptotic thermal entanglement proceeds via a series of phase transitions in the local relaxation rate, which is a consequence of nonHermiticity. In particular, non-Hermiticity can cause the rate to be either faster or, even more interestingly, slower than predicted by the matrix eigenvalue gap. This result is caused by expansion coefficients that grow exponentially with system size, resulting in a "phantom" eigenvalue and is due to nonorthogonality of non-Hermitian eigenvectors. We numerically demonstrate that the phenomenon also occurs in random circuits with nonoptimal generic gates, random U(4) gates, and also without spatial or temporal randomness, suggesting that it could be of wide importance in other non-Hermitian settings, including correlations.