Abstract
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 proved 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 non-Hermiticity. 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 is caused by an exponential in system size explosion of expansion coefficient sizes resulting in a 'phantom' eigenvalue, and is due to non-orthogonality of non-Hermitian eigenvectors. We numerically demonstrate that the phenomenon occurs also in random circuits with non-optimal generic gates, random U(4) gates, and also without spatial or temporal randomness, suggesting that it could be of wide importance also in other non-Hermitian settings, including correlations.
Highlights
Entanglement is one of the key properties that can make quantum systems different than classical ones, which is reflected in quantum information—large entanglement is a necessary resource to gain an advantage over classical computation, and many of the new phases discovered in recent decades can be distinguished by different patterns of entanglement [1]
Our fastest circuit is significantly faster than the best previous random circuits. (ii) We identify a number of phase transitions in time—at certain moments, the convergence rate to the asymptotic “thermal” entanglement of random states suddenly changes
The protocols that we study are composed of commuting groups of 2-qubit gates denoted by four letters: A, B, C, and D
Summary
Entanglement is one of the key properties that can make quantum systems different than classical ones, which is reflected in quantum information—large entanglement is a necessary resource to gain an advantage over classical computation, and many of the new phases discovered in recent decades can be distinguished by different patterns of entanglement [1]. How can one efficiently generate this resource? We focus on the so-called random quantum circuits [2], where quantum gates are chosen randomly from a certain set of gates. What set one uses might foremost depend on the available resources; while one wants to generate entanglement as quickly as possible, one must use the resources as efficiently as possible
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