Entanglement Domain Walls in Monitored Quantum Circuits and the Directed Polymer in a Random Environment

Abstract

Monitored quantum dynamics reveal quantum state trajectories which exhibit a rich phenomenology of entanglement structures, including a transition from a weakly-monitored volume law entangled phase to a strongly-monitored area law phase. For one-dimensional hybrid circuits with both random unitary dynamics and interspersed measurements, we combine analytic mappings to an effective statistical mechanics model with extensive numerical simulations on hybrid Clifford circuits to demonstrate that the universal entanglement properties of the volume law phase can be quantitatively described by a fluctuating entanglement domain wall that is equivalent to a "directed polymer in a random environment" (DPRE). This relationship improves upon a qualitative "mean-field" statistical mechanics of the volume-law-entangled phase [1, 2]. For the Clifford circuit in various geometries, we obtain agreement between the subleading entanglement entropies and error correcting properties of the volume-law phase (which quantify its stability to projective measurements) with predictions of the DPRE. We further demonstrate that depolarizing noise in the hybrid dynamics near the final circuit time can drive a continuous phase transition to a non-error correcting volume law phase that is not immune to the disentangling action of projective measurements. We observe this transition in hybrid Clifford dynamics, and obtain quantitative agreement with critical exponents for a "pinning" phase transition of the DPRE in the presence of an attractive interface.

22 pages, 18 figures

References in corpus (5)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Critical properties of the measurement-induced transition in random quantum circuits
• Statistical mechanics of quantum error correcting codes
• How Dynamical Quantum Memories Forget
• Quantum coding with low-depth random circuits

Cited by in corpus (49)

• Measurement-induced entanglement and teleportation on a noisy quantum processor
• Cross Entropy Benchmark for Measurement-Induced Phase Transitions
• Entanglement phase transitions in random stabilizer tensor networks
• Purification Timescales in Monitored Fermions
• Simulating a measurement-induced phase transition for trapped ion circuits
• Majorana Loop Models for Measurement-Only Quantum Circuits
• Universal KPZ scaling in noisy hybrid quantum circuits
• Decodable hybrid dynamics of open quantum systems with Z_2 symmetry
• Entanglement Structure and Information Protection in Noisy Hybrid Quantum Circuits
• Measurement-induced phase transitions in sparse nonlocal scramblers
• Crystalline Quantum Circuits
• Interactions and integrability in weakly monitored Hamiltonian systems
• Entanglement Growth and Minimal Membranes in $(d+1)$ Random Unitary Circuits
• Boundary transfer matrix spectrum of measurement-induced transitions
• Efficient sampling of noisy shallow circuits via monitored unraveling
• The entanglement membrane in exactly solvable lattice models
• Renormalization group for measurement and entanglement phase transitions
• Field theory of monitored, interacting fermion dynamics with charge conservation
• Measurement induced criticality in quasiperiodic modulated random hybrid circuits
• Zero-temperature entanglement membranes in quantum circuits
• Classifying One-Dimensional Quantum States Prepared by a Single Round of Measurements
• Statistical Mechanics of Monitored Dissipative Random Circuits
• Steering-induced phase transition in measurement-only quantum circuits
• Subsystem Information Capacity in Random Circuits and Hamiltonian Dynamics
• Protect Measurement-Induced Phase Transition from Noise
• Entanglement dynamics in U(1) symmetric hybrid quantum automaton circuits
• Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
• Designs from magic-augmented Clifford circuits
• Phase transition in von Neumann entanglement entropy from replica symmetry breaking
• Onset of scrambling as a dynamical transition in tunable-range quantum circuits
• Decoding the Entanglement Structure of Monitored Quantum Circuits
• Petz map recovery for long-range entangled quantum many-body states
• Phase transitions in sampling and error correction in local Brownian circuits
• Charge and Spin Sharpening Transitions on Dynamical Quantum Trees
• Coherent Information Phase Transition in a Noisy Quantum Circuit
• Monitored Fluctuating Hydrodynamics
• Measurement-Driven Transitions between Area Law Phases
• Concomitant Entanglement and Control Criticality Driven by Collective Measurements
• Random Quantum Circuits with Time-Reversal Symmetry
• Dynamically generated concatenated codes and their phase diagrams
• Universality classes for purification in nonunitary quantum processes
• Multipartite Greenberger-Horne-Zeilinger Entanglement in Monitored Random Clifford Circuits
• Pseudoentanglement from tensor networks
• Neural network enhanced cross entropy benchmark for monitored circuits
• Roughening Transition in Quantum Circuits
• Noisy Monitored Quantum Circuits
• Engineering entanglement geometry via spacetime-modulated measurements
• Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions
• Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout