Entanglement Growth and Minimal Membranes in $(d+1)$ Random Unitary Circuits

Abstract

Understanding the nature of entanglement growth in many-body systems is one of the fundamental questions in quantum physics. Here, we study this problem by characterizing the entanglement fluctuations and distribution of $(d+1)$ qubit lattice evolved under a random unitary circuit. Focusing on Clifford gates, we perform extensive numerical simulations of random circuits in $1\le d\le 4$ dimensions. Our findings demonstrate that properties of growth of bipartite entanglement entropy are characterized by the roughening exponents of a $d$-dimensional membrane in a $(d+1)$ elastic medium.

4 pages

References in corpus (33)

• The density-matrix renormalization group in the age of matrix product states
• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Black holes as mirrors: quantum information in random subsystems
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• Random Quantum Circuits
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Critical properties of the measurement-induced transition in random quantum circuits
• Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Holographic Evolution of Entanglement Entropy
• Ground state entanglement and geometric entropy in the Kitaev's model
• Challenges to observation of many-body localization
• Operator scaling dimensions and multifractality at measurement-induced transitions
• Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains
• Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions
• Bridging entanglement dynamics and chaos in semiclassical systems
• Measurement-induced phase transitions in $(d+1)$-dimensional stabilizer circuits
• Eigenstate Thermalization Hypothesis and Free Probability
• Measurement-Induced Power-Law Negativity in an Open Monitored Quantum Circuit
• Exact convergence times for generation of random bipartite entanglement
• Entanglement Domain Walls in Monitored Quantum Circuits and the Directed Polymer in a Random Environment
• Controlling entanglement at absorbing state phase transitions in random circuits
• Scrambling Transition in a Radiative Random Unitary Circuit
• Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality
• Thermalization of entanglement
• Entanglement Typicality
• Majorana Loop Models for Measurement-Only Quantum Circuits
• Transport and entanglement growth in long-range random Clifford circuits
• Renormalization group for measurement and entanglement phase transitions
• Absence of localization in two-dimensional Clifford circuits

Cited by in corpus (16)

• Many-Body Localization in the Age of Classical Computing
• Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
• Hilbert space delocalization under random unitary circuits
• The entanglement membrane in exactly solvable lattice models
• Zero-temperature entanglement membranes in quantum circuits
• Steering-induced phase transition in measurement-only quantum circuits
• Bulk-Measurement-Induced Boundary Phase Transition in Toric Code and Gauge-Higgs Model
• Subsystem Information Capacity in Random Circuits and Hamiltonian Dynamics
• Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks
• Measurement-only dynamical phase transition of topological and boundary order in toric code and gauge-Higgs models
• Approximate inverse measurement channel for shallow shadows
• Hierarchy of emergent cluster states by measurement from symmetry-protected-topological states with large symmetry to subsystem cat state
• Relaxation Critical Dynamics in Measurement-induced Phase Transitions
• Anticoncentration in Clifford Circuits and Beyond: From Random Tensor Networks to Pseudo-Magic States
• Entanglement dynamics from universal low-lying modes
• Roughening Transition in Quantum Circuits