Variational approach to open quantum systems with long-range competing interactions

Abstract

Competition between short- and long-range interactions underpins many emergent phenomena in nature. Despite rapid progress in their experimental control, computational methods capable of accurately simulating open quantum many-body systems with complex long-ranged interactions at scale remain scarce. Here, we address this limitation by introducing an efficient and scalable approach to dissipative quantum lattices in one and two dimensions, combining matrix product operators and time-dependent variational Monte Carlo. We showcase the versatility, effectiveness, and unique methodological advantages of our algorithm by simulating the non-equilibrium dynamics and steady states of spin-$\frac{1}{2}$ lattices with competing algebraically-decaying interactions for as many as $N=200$ sites, revealing the emergence of spatially-modulated magnetic order far from equilibrium. This approach offers promising prospects for advancing our understanding of the complex non-equilibrium properties of a diverse variety of experimentally-realizable quantum systems with long-ranged interactions, including Rydberg atoms, ultracold dipolar molecules, and trapped ions.

References in corpus (56)

• The density-matrix renormalization group in the age of matrix product states
• Observation of a Discrete Time Crystal
• Observation of discrete time-crystalline order in a disordered dipolar many-body system
• Floquet Time Crystals
• Time-dependent variational principle for quantum lattices
• A Rydberg Quantum Simulator
• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Time-evolution methods for matrix-product states
• High-fidelity parallel entangling gates on a neutral atom quantum computer
• High-power collective charging of a solid-state quantum battery
• Theory of variational quantum simulation
• Quantum phases from competing short- and long-range interactions in an optical lattice
• Controlling many-body dynamics with driven quantum scars in Rydberg atom arrays
• Long-range interacting quantum systems
• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• Quantum many-body dynamics in two dimensions with artificial neural networks
• New frontiers with quantum gases of polar molecules
• 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
• QuantumOptics.jl: A Julia framework for simulating open quantum systems
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Dipolar Exchange Quantum Logic Gate with Polar Molecules
• Many-body dynamics of dipolar molecules in an optical lattice
• Variational principle for steady states of dissipative quantum many-body systems
• Constructing neural stationary states for open quantum many-body systems
• Variational quantum Monte Carlo simulations with tensor-network states
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Depolarization dynamics in a strongly interacting solid-state spin ensemble
• 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
• Observing emergent hydrodynamics in a long-range quantum magnet
• Quantum criticality in a metallic spin liquid
• Dipolar quantum solids emerging in a Hubbard quantum simulator
• Monte Carlo simulation with Tensor Network States
• Antiferromagnetic long-range order in dissipative Rydberg lattices
• Probing many-body dynamics in a two dimensional dipolar spin ensemble
• Fundamentals of Quantum Mechanics in Liouville Space
• Frustrating quantum batteries
• Steady States of Infinite-Size Dissipative Quantum Chains via Imaginary Time Evolution
• Dissipative time crystals with long-range Lindbladians
• Accurate simulation for finite projected entangled pair states in two dimensions
• Many-Body Open Quantum Systems
• Finding the ground state of a lattice gauge theory with fermionic tensor networks: a $2+1d$ ${\mathbb{Z}}_2$ demonstration
• A scheme for automatic differentiation of complex loss functions
• A Variational Ansatz for the Ground State of the Quantum Sherrington-Kirkpatrick Model
• Analysis of a density matrix renormalization group approach for transport in open quantum systems
• Ultracold LiCr: a new pathway to quantum gases of paramagnetic polar molecules
• Accurate Simulation of the Hubbard Model with Finite Fermionic Projected Entangled Pair States
• Quantum Phases from Competing Van der Waals and Dipole-Dipole Interactions of Rydberg Atoms
• Driven-dissipative Rydberg blockade in optical lattices
• Deep Neural Networks as Variational Solutions for Correlated Open Quantum Systems
• Quantum Transport in Open Spin Chains using Neural-Network Quantum States
• Density Matrix Renormalization Group Algorithm For Mixed Quantum States
• Variational Neural and Tensor Network Approximations of Thermal States
• Tensor-network-based variational Monte Carlo approach to the non-equilibrium steady state of open quantum systems