



01546nas a2200145   4500008004100000245006600041210006600107260001400173520107500187100001801262700002601280700003201306700002501338856003701363       2020                        eng d00aClassical Models of Entanglement in Monitored Random Circuits0 aClassical Models of Entanglement in Monitored Random Circuits  c4/14/20203 a<p>The evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements shows versatile behavior, with connections to phase transitions and complexity theory. We reformulate the problem in terms of a classical Markov process for the dynamics of bipartition purities and establish a probabilistic cellular-automaton algorithm to compute entanglement entropy in monitored random circuits on arbitrary graphs. In one dimension, we further relate the evolution of the entropy to a simple classical spin model that naturally generalizes a two-dimensional lattice percolation problem. We also establish a Markov model for the evolution of the zeroth Rényi entropy and demonstrate that, in one dimension and in the limit of large local dimension, it coincides with the corresponding second-Rényi-entropy model. Finally, we extend the Markovian description to a more general setting that incorporates continuous-time dynamics, defined by stochastic Hamiltonians and weak local measurements continuously monitoring the system.</p>1 aShtanko, Oles1 aKharkov, Yaroslav, A.1 aGarcía-Pintos, Luis, Pedro1 aGorshkov, Alexey, V.  uhttps://arxiv.org/abs/2004.06736