Entanglement Dynamics of Noisy Random Circuits

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.

References in corpus (4)

• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Measurement-Induced Power-Law Negativity in an Open Monitored Quantum Circuit
• Upper bounds on entangling rates of bipartite Hamiltonians
• Integrable nonunitary open quantum circuits

Cited by in corpus (15)

• Channeling quantum criticality
• Entanglement Structure and Information Protection in Noisy Hybrid Quantum Circuits
• Noise-induced phase transitions in hybrid quantum circuits
• Robustness of quantum chaos and anomalous relaxation in open quantum circuits
• Efficient sampling of noisy shallow circuits via monitored unraveling
• Statistical Mechanics of Monitored Dissipative Random Circuits
• Locally purified density operators for noisy quantum circuits
• Random insights into the complexity of two-dimensional tensor network calculations
• Universal Spreading of Conditional Mutual Information in Noisy Random Circuits
• Phase transitions in sampling and error correction in local Brownian circuits
• Superiority in dense coding through non-Markovian stochasticity
• Limitations of Noisy Quantum Devices in Computational and Entangling Power
• Increasing extractable work in small qubit landscapes
• Measurement-induced entanglement in noisy 2D random circuits
• Noisy Monitored Quantum Circuits