Entanglement dynamics of noisy random circuits

The process by which open quantum systems thermalize with an environment is both of fundamental interest and relevant to noisy quantum devices. As a minimal model of this process, we consider a qudit chain evolving under local random unitaries and local depolarization channels. After mapping to a statistical mechanics model, the depolarization (noise) acts like a symmetry-breaking field, and we argue that it causes the system to thermalize within a timescale independent of system size. We show that various bipartite entanglement measures-mutual information, operator entanglement, and entanglement negativity-grow at a speed proportional to the size of the bipartition boundary. As a result, these entanglement measures obey an area law: Their maximal value during the dynamics is bounded by the boundary instead of the volume. In contrast, if the depolarization only acts at the system boundary, then the maximum value of the entanglement measures obeys a volume law. We complement our analysis with scalable simulations involving Clifford gates, for both one- and two-dimensional systems.

Automated summary

This study investigates the thermalization process of open quantum systems with an environment, using a qudit chain subjected to local random unitaries and local depolarization channels as a minimal model. It is found that the depolarization leads to thermalization within a timescale independent of system size, acting like a symmetry-breaking field in the statistical mechanics model. The study further shows that various entanglement measures exhibit an area law by growing at a speed proportional to the size of the bipartition boundary.