@article {2565, title = {Classical Models of Entanglement in Monitored Random Circuits}, year = {2020}, month = {4/14/2020}, abstract = {

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 R{\'e}nyi entropy and demonstrate that, in one dimension and in the limit of large local dimension, it coincides with the corresponding second-R{\'e}nyi-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.

}, url = {https://arxiv.org/abs/2004.06736}, author = {Oles Shtanko and Yaroslav A. Kharkov and Luis Pedro Garc{\'\i}a-Pintos and Alexey V. Gorshkov} }