Efficient simulation of non-trivial dissipative spin chains via stochastic unraveling

Abstract

We present a new technique for efficiently simulating (in polynomial time) a class of one-dimensional (1D) dissipative spin chains that, when mapped to fermions, have quadratic Hamiltonians, with the only nonlinearity coming from Jordan-Wigner strings appearing in the jump operators, despite the fact that these models cannot be mapped to quadratic fermionic master equations. We show that many such Lindblad master equations admit an exact stochastic unraveling, with individual trajectories evolving as Gaussian fermionic states, even though the full master equation describes a system inequivalent to free fermions. This allows one to calculate arbitrary observables efficiently without sign problems, and with bounded sampling complexity. We utilize this new technique to study three paradigmatic dissipative effects: the melting of antiferromagnetic order in the presence of local loss, many-body subradiant phenomenon in systems with correlated loss, and nonequilibrium steady states of a 1D dissipative transverse-field Ising model. Beyond simply providing a powerful numerical technique, our method can also be used to gain both qualitative and quantitative insights into the role of interactions in these models.

29 pages, 11 figures

References in corpus (38)

• Quantum Computing in the NISQ era and beyond
• Mixed State Entanglement and Quantum Error Correction
• Anyons in an exactly solved model and beyond
• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• Evolution of Entanglement Entropy in One-Dimensional Systems
• An Area Law for One Dimensional Quantum Systems
• Gaussian Boson Sampling
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Exponential improvement in photon storage fidelities using subradiance and "selective radiance" in atomic arrays
• Finite-temperature transport in one-dimensional quantum lattice models
• Entanglement Entropy dynamics in Heisenberg chains
• Classical simulation of noninteracting-fermion quantum circuits
• Exact nonequilibrium steady state of a strongly driven open XXZ chain
• Disorder-Free Localization
• Storing light with subradiant correlations in arrays of atoms
• Theory of Subradiant States of a One-Dimensional Two-Level Atom Chain
• Atom-light interactions in quasi-1D nanostructures: a Green's function perspective
• Subradiant states of quantum bits coupled to a one-dimensional waveguide
• Dissipative Dynamics and Phase Transitions in Fermionic Systems
• A Quantum to Classical Phase Transition in Noisy Quantum Computers
• Critical open-system dynamics in a one-dimensional optical lattice clock
• Optimization of photon storage fidelity in ordered atomic arrays
• Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems
• The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
• Closed form solution of Lindblad master equations without gain
• Exceptional Spin Liquids from Couplings to the Environment
• Quantum correlations in the 1-D driven dissipative transverse field XY model
• Subradiant emission from regular atomic arrays: universal scaling of decay rates from the generalized Bloch theorem
• Quantum Criticality in Open Quantum Spin Chains with Nonreciprocity
• Entanglement-Optimal Trajectories of Many-Body Quantum Markov Processes
• Quantum nonreciprocal interactions via dissipative gauge symmetry
• Exterior integrability: Yang-Baxter form of nonequilibrium steady state density operator
• Absence of logarithmic and algebraic scaling entanglement phases due to skin effect
• Absence of measurement-induced entanglement transition due to feedback-induced skin effect
• Dynamical Transition due to Feedback-induced Skin Effect
• Complexity of Fermionic Dissipative Interactions and Applications to Quantum Computing
• Free-Fermion Multiply Excited Eigenstates and Their Experimental Signatures in 1D Arrays of Two-Level Atoms
• Hidden time-reversal in driven XXZ spin chains: exact solutions and new dissipative phase transitions