Jaš Bensa: Fastest local entanglement scrambler, multistage thermalization, and a non-Hermitian phantom

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. The optimal gate and the protocol that generates entanglement the fastest is identified. Relaxation towards the asymptotic thermal entanglement proceeds via a series of phase transitions in the local relaxation rate, which are 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 gap. This is caused by a many-body explosion of expansion coefficients due to non-orthogonality which can result in a 'phantom' eigenvalue and could be of interest in other non-Hermitian settings.