Entanglement dynamics in hybrid quantum circuits

Abstract

The central philosophy of statistical mechanics (stat-mech) and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple universal "laws". This same philosophy promises powerful methods for studying the dynamics of quantum information in ideal and noisy quantum circuits -- for which classical description of individual circuits is expected to be generically intractable. Here, we review recent progress in understanding the dynamics of quantum information in ensembles of random quantum circuits, through a stat-mech lens. We begin by reviewing discoveries of universal features of entanglement growth, operator spreading, thermalization, and chaos in unitary random quantum circuits, and their relation to stat-mech problems of random surface growth and noisy hydrodynamics. We then explore the dynamics of monitored random circuits, which can loosely be thought of as noisy dynamics arising from an environment monitoring the system, and exhibit new types of measurement-induced phases and criticality. Throughout, we attempt to give a pedagogical introduction to various technical methods, and to highlight emerging connections between concepts in stat-mech, quantum information and quantum communication theory.

v2: various updated sections, new figures. Chapter in "Springer volume: Entanglement in Spin Chains -- Theory and Quantum Technology Applications"

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Cited by in corpus (38)

• Random Quantum Circuits
• Measurement-induced entanglement and teleportation on a noisy quantum processor
• Volume-to-Area Law Entanglement Transition in a non-Hermitian Free Fermionic Chain
• Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer
• Solvable model of deep thermalization with distinct design times
• Phase transition in magic with random quantum circuits
• Scrambling Transition in a Radiative Random Unitary Circuit
• Tight bounds on the convergence of noisy random circuits to the uniform distribution
• Probing sign structure using measurement-induced entanglement
• Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP and Free Probability
• Neural-Network Decoders for Measurement Induced Phase Transitions
• Transport and entanglement growth in long-range random Clifford circuits
• Many-Body Open Quantum Systems
• Entanglement dynamics with string measurement operators
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain
• Chaos and magic in the dissipative quantum kicked top
• The impact of different unravelings in a monitored system of free fermions
• Entanglement and absorbing state transitions in $(d+1)$-dimensional stabilizer circuits
• Dynamics of Pseudoentanglement
• Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information
• Magic transition in measurement-only circuits
• Measurement-induced multipartite-entanglement regimes in collective spin systems
• Purity decay rate in random circuits with different configurations of gates
• Non-Abelian entanglement asymmetry in random states
• Critical Properties of Weak Measurement Induced Phase Transitions in Random Quantum Circuits
• Charge and Spin Sharpening Transitions on Dynamical Quantum Trees
• Effective field theory of random quantum circuits
• Approximate inverse measurement channel for shallow shadows
• Topology and Spectrum in Measurement-Induced Phase Transitions
• Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements
• Non-unitarity maximizing unraveling of open quantum dynamics
• Qubit Vitrification and Entanglement Criticality on a Quantum Simulator
• Observable Measurement-Induced Transitions
• Quantum-limited generalized measurement for tunnel-coupled condensates
• Noise resilience in adaptive and symmetric monitored quantum circuits
• Universality classes for purification in nonunitary quantum processes
• Information Bounds on phase transitions in disordered systems
• Non-Equilibrium Quantum Many-Body Physics with Quantum Circuits