Entanglement-Optimal Trajectories of Many-Body Quantum Markov Processes

Abstract

We develop a novel approach aimed at solving the equations of motion of open quantum many-body systems. It is based on a combination of generalized wave function trajectories and matrix product states. We introduce an adaptive quantum stochastic propagator, which minimizes the expected entanglement in the many-body quantum state, thus minimizing the computational cost of the matrix product state representation of each trajectory. We illustrate this approach on the example of a one-dimensional open Brownian circuit. We show that this model displays an entanglement phase transition between area and volume law when changing between different propagators and that our method autonomously finds an efficiently representable area law unravelling.

References in corpus (30)

• Quantum Computing in the NISQ era and beyond
• Entanglement of Formation of an Arbitrary State of Two Qubits
• The density-matrix renormalization group in the age of matrix product states
• Efficient classical simulation of slightly entangled quantum computations
• Real time evolution using the density matrix renormalization group
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Quantum trajectories and open many-body quantum systems
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Measurement-driven entanglement transition in hybrid quantum circuits
• Theory of the phase transition in random unitary circuits with measurements
• Unitary-projective entanglement dynamics
• Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
• Critical properties of the measurement-induced transition in random quantum circuits
• Scalable probes of measurement-induced criticality
• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• Entanglement phase transitions in measurement-only dynamics
• Simulation methods for open quantum many-body systems
• Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems
• Variational neural network ansatz for steady states in open quantum systems
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems
• Constructing neural stationary states for open quantum many-body systems
• A positive tensor network approach for simulating open quantum many-body systems
• Measurement-induced dark state phase transitions in long-ranged fermion systems
• Operator scaling dimensions and multifractality at measurement-induced transitions
• Quantum dynamics of thermalizing systems
• Nonequilibrium Steady-State Transport in Quantum Impurity Models: a Thermofield and Quantum Quench Approach using Matrix Product States
• Engineered dissipation induced entanglement transition in quantum spin chains: from logarithmic growth to area law
• Linked cluster expansions for open quantum systems on a lattice

Cited by in corpus (30)

• Many-Body Open Quantum Systems
• Comparing bipartite entropy growth in open-system matrix-product simulation methods
• Efficient sampling of noisy shallow circuits via monitored unraveling
• Measurement-Induced Quantum Synchronization and Multiplexing
• Adaptive Trotterization for time-dependent Hamiltonian quantum dynamics using piecewise conservation laws
• Monte Carlo matrix-product-state approach to the false vacuum decay in the monitored quantum Ising chain
• Optimized trajectory unraveling for classical simulation of noisy quantum dynamics
• Unraveling Dicke Superradiant Decay with Separable Coherent Spin States
• Unraveling superradiance: Entanglement and mutual information in collective decay
• Dynamical heterogeneity and large deviations in the open quantum East glass model from tensor networks
• Monitoring-induced Entanglement Entropy and Sampling Complexity
• Boundary Time Crystals Induced by Local Dissipation and Long-Range Interactions
• Open quantum dynamics with variational non-Gaussian states and the truncated Wigner approximation
• Large-scale stochastic simulation of open quantum systems
• Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements
• Non-unitarity maximizing unraveling of open quantum dynamics
• Space-time correlations in monitored kinetically constrained discrete-time quantum dynamics
• Tensor-network-based variational Monte Carlo approach to the non-equilibrium steady state of open quantum systems
• Purification Dynamics in a Continuous-time Hybrid Quantum Circuit Model
• Qubit-environment entanglement in time-dependent pure dephasing
• Is there any reasonable dynamics for quantum subsystems within the unitary-only quantum theory?
• Analog simulation of noisy quantum circuits
• Efficient circular Dyson Brownian motion algorithm
• Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories?
• Absence of measurement- and unraveling-induced entanglement transitions in continuously monitored one-dimensional free fermions
• Theoretical Limits of Protocols for Distinguishing Different Unravelings
• Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings
• Dynamically Optimal Unraveling Schemes for Simulating Lindblad Equations
• Rydberg Atoms in a Ladder Geometry: Quench Dynamics and Floquet Engineering
• Efficient simulation of non-trivial dissipative spin chains via stochastic unraveling