Entanglement Dynamics of Noisy Random Circuits

TL;DR

This paper studies how noise affects entanglement growth in random quantum circuits, showing that depolarization leads to area-law entanglement scaling and rapid thermalization, with implications for noisy quantum devices.

Contribution

It introduces a statistical mechanics model of noisy quantum circuits, revealing how depolarization induces thermalization and influences entanglement scaling laws.

Findings

Depolarization acts like a symmetry-breaking field causing rapid thermalization.

Entanglement measures grow proportionally to boundary size, obeying an area law.

Boundary-only depolarization results in volume-law entanglement maximums.

Abstract

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.