Classical Models of Entanglement in Monitored Random Circuits

• URL: http://arxiv.org/abs/2004.06736v1
• Date: Tue, 14 Apr 2020 18:00:14 GMT
• Title: Classical Models of Entanglement in Monitored Random Circuits
• Authors: Oles Shtanko, Yaroslav A. Kharkov, Luis Pedro Garc\'ia-Pintos, Alexey V. Gorshkov
• Abstract summary: We show the evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements. We also establish a Markov model for the evolution of the zeroth R'enyi entropy and demonstrate that, in one dimension and in the limit of large local dimension, it coincides with the corresponding second-R'enyi-entropy model.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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