Tensor-network-based variational Monte Carlo approach to the non-equilibrium steady state of open quantum systems
arXiv:2405.12044 · doi:10.22331/q-2024-09-17-1475
Abstract
We introduce a novel method of efficiently simulating the non-equilibrium steady state of large many-body open quantum systems with highly non-local interactions, based on a variational Monte Carlo optimization of a matrix product operator ansatz. Our approach outperforms and offers several advantages over comparable algorithms, such as an improved scaling of the computational cost with respect to the bond dimension for periodic systems. We showcase the versatility of our approach by studying the phase diagrams and correlation functions of the dissipative quantum Ising model with collective dephasing and long-ranged power law interactions for spin chains of up to spins.
References in corpus (96)
- The density-matrix renormalization group in the age of matrix product states
- Quantum sensing
- Quantum Simulation
- Efficient classical simulation of slightly entangled quantum computations
- Decoherence Free Subspaces for Quantum Computation
- The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics
- Observation of a Discrete Time Crystal
- Matrix Product Density Operators: Simulation of finite-T and dissipative systems
- Quantum trajectories and open many-body quantum systems
- Observation of entanglement propagation in a quantum many-body system
- Programmable Quantum Simulations of Spin Systems with Trapped Ions
- Realizing quantum Ising models in tunable two-dimensional arrays of single Rydberg atoms
- Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
- Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
- Observation of mesoscopic crystalline structures in a two-dimensional Rydberg gas
- Quantum Computing Using Dissipation to Remain in a Decoherence-Free Subspace
- Quantum Decoherence
- Corner Transfer Matrix Renormalization Group Method
- The Kerr-Cat Qubit: Stabilization, Readout, and Gates
- Entropy scaling and simulability by Matrix Product States
- Quantum Entanglement in Neural Network States
- Studying Two Dimensional Systems With the Density Matrix Renormalization Group
- Quantum simulation and computing with Rydberg-interacting qubits
- Long-range interacting quantum systems
- Hardware-efficient autonomous quantum error correction
- Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
- Optimization of quantum Monte Carlo wave functions by energy minimization
- Quantum Approximate Optimization of the Long-Range Ising Model with a Trapped-Ion Quantum Simulator
- Open quantum systems with local and collective incoherent processes: Efficient numerical simulation using permutational invariance
- Engineered Dissipation for Quantum Information Science
- Matrix product simulations of non-equilibrium steady states of quantum spin chains
- 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
- Strict Detailed Balance is Unnecessary in Monte Carlo Simulation
- Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
- Unconventional magnetism via optical pumping of interacting spin systems
- Variational principle for steady states of dissipative quantum many-body systems
- Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems
- A positive tensor network approach for simulating open quantum many-body systems
- Constructing neural stationary states for open quantum many-body systems
- Variational quantum Monte Carlo simulations with tensor-network states
- Repetition Cat Qubits for Fault-Tolerant Quantum Computation
- Protecting a Bosonic Qubit with Autonomous Quantum Error Correction
- Kinetic constraints, hierarchical relaxation and onset of glassiness in strongly interacting and dissipative Rydberg gases
- A simple tensor network algorithm for two-dimensional steady states
- A Matrix-Product-Operator Approach to the Nonequilibrium Steady State of Driven-Dissipative Quantum Arrays
- Stabilizing entanglement via symmetry-selective bath engineering in superconducting qubits
- Scalable Dissipative Preparation of Many-Body Entanglement
- Out-of-equilibrium structures in strongly interacting Rydberg gases with dissipation
- Dissipative preparation of Chern insulators
- Anomalous broadening in driven dissipative Rydberg systems
- Low-overhead fault-tolerant quantum computing using long-range connectivity
- Perturbative approach to Markovian open quantum systems
- Purifications of multipartite states: limitations and constructive methods
- Non-equilibrium dynamics of Ising models with decoherence: an exact solution
- Tensor network techniques for the computation of dynamical observables in 1D quantum spin systems
- Comparing and combining measurement-based and driven-dissipative entanglement stabilization
- Generalized Schrieffer-Wolff Formalism for Dissipative Systems
- Bose-Hubbard Model: Relation Between Driven-Dissipative Steady-States and Equilibrium Quantum Phases
- One-dimensional many-body entangled open quantum systems with tensor network methods
- Fundamentals of Quantum Mechanics in Liouville Space
- A solvable family of driven-dissipative many-body systems
- Coherent and dissipative dynamics of entangled few-body systems of Rydberg atoms
- Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws
- Mean-field validity in a dissipative critical system: Liouvillian gap, -symmetric antigap, and permutational symmetry in the model
- Linked cluster expansions for open quantum systems on a lattice
- Continuous Symmetry Breaking in a Trapped-Ion Spin Chain
- Long-range coupling and scalable architecture for superconducting flux qubits
- Steady States of Infinite-Size Dissipative Quantum Chains via Imaginary Time Evolution
- Dissipative time crystals with long-range Lindbladians
- Entanglement-Optimal Trajectories of Many-Body Quantum Markov Processes
- Fundamental limitations in the purifications of tensor networks
- Dissipation induced dipole blockade and anti-blockade in driven Rydberg systems
- Realistic simulations of spin squeezing and cooperative coupling effects in large ensembles of interacting two-level systems
- Dynamical and Steady State Properties of a Bose-Hubbard Chain with Bond-Dissipation: A Study based on Matrix Product Operators
- Phase-Space Methods for Simulating the Dissipative Many-Body Dynamics of Collective Spin Systems
- Long-range connectivity in a superconducting quantum processor using a ring resonator
- Fully quantum scalable description of driven dissipative lattice models
- Dissipative preparation and stabilization of many-body quantum states in a superconducting qutrit array
- Driven-dissipative criticality within the discrete truncated Wigner approximation
- Low rank approximation for the numerical simulation of high dimensional Lindblad and Riccati equations
- Driven-dissipative Ising Model: An exact field-theoretical analysis
- Exact solution of the infinite-range dissipative transverse-field Ising model
- Photon propagation through dissipative Rydberg media at large input rates
- Analysis of a density matrix renormalization group approach for transport in open quantum systems
- Beating the House: Fast Simulation of Dissipative Quantum Systems with Ensemble Rank Truncation
- Monte Carlo matrix-product-state approach to the false vacuum decay in the monitored quantum Ising chain
- Driven-dissipative Rydberg blockade in optical lattices
- Adaptive variational low-rank dynamics for open quantum systems
- Deep Neural Networks as Variational Solutions for Correlated Open Quantum Systems
- Crossover from the discontinuous to continuous phase transitions in dissipative spin system with collective decay
- Quantum Transport in Open Spin Chains using Neural-Network Quantum States
- Density Matrix Renormalization Group Algorithm For Mixed Quantum States
- Liouville Space Neural Network Representation of Density Matrices
- Bosonic representation of a Lipkin-Meshkov-Glick model with Markovian dissipation