A quantum algorithm for the direct estimation of the steady state of open quantum systems

Abstract

Simulating the dynamics and the non-equilibrium steady state of an open quantum system are hard computational tasks on conventional computers. For the simulation of the time evolution, several efficient quantum algorithms have recently been developed. However, computing the non-equilibrium steady state as the long-time limit of the system dynamics is often not a viable solution, because of exceedingly long transient features or strong quantum correlations in the dynamics. Here, we develop an efficient quantum algorithm for the direct estimation of averaged expectation values of observables on the non-equilibrium steady state, thus bypassing the time integration of the master equation. The algorithm encodes the vectorized representation of the density matrix on a quantum register, and makes use of quantum phase estimation to approximate the eigenvector associated to the zero eigenvalue of the generator of the system dynamics. We show that the output state of the algorithm allows to estimate expectation values of observables on the steady state. Away from critical points, where the Liouvillian gap scales as a power law of the system size, the quantum algorithm performs with exponential advantage compared to exact diagonalization.

arXiv comment18 pages, 5 figures, to appear in Quantum journal

References in corpus (50)

• A variational eigenvalue solver on a quantum processor
• Elementary gates for quantum computation
• Quantum algorithm for solving linear systems of equations
• The theory of variational hybrid quantum-classical algorithms
• Quantum fluids of light
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• An Open-System Quantum Simulator with Trapped Ions
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• A Theory of Trotter Error
• New class of quantum error-correcting codes for a bosonic mode
• Spectral theory of Liouvillians for dissipative phase transitions
• IBM Q Experience as a versatile experimental testbed for simulating open quantum systems
• Quantum simulations and many-body physics with light
• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• 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
• Quantum Simulation with Interacting Photons
• Optimal Quantum Measurements of Expectation Values of Observables
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Relaxation times of dissipative many-body quantum systems
• The problem of equilibration and the computation of correlation functions on a quantum computer
• A positive tensor network approach for simulating open quantum many-body systems
• Constructing neural stationary states for open quantum many-body systems
• Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise
• A quantum algorithm for evolving open quantum dynamics on quantum computing devices
• A dissipative quantum Church-Turing theorem
• Quantum computers as universal quantum simulators: state-of-art and perspectives
• A simple tensor network algorithm for two-dimensional steady states
• Quantum critical regime in a quadratically-driven nonlinear photonic lattice
• A Matrix-Product-Operator Approach to the Nonequilibrium Steady State of Driven-Dissipative Quantum Arrays
• Quantum algorithm for simulating the dynamics of an open quantum system
• Corner space renormalization method for driven-dissipative 2D correlated systems
• Approximate Quantum Fourier Transform with $O(n\log (n))$ T gates
• Time-dependent generalized Gibbs ensembles in open quantum systems
• Improving the Performance of Deep Quantum Optimization Algorithms with Continuous Gate Sets
• Critical behavior of dissipative two-dimensional spin lattices
• On the uniqueness of the steady-state solution of the Lindblad-Gorini-Kossakowski-Sudarshan equation
• Universal simulation of Markovian open quantum systems
• Digital quantum simulation of many-body non-Markovian dynamics
• Linked cluster expansions for open quantum systems on a lattice
• Variational Quantum Algorithm for Non-equilibrium Steady States
• A driven-dissipative quantum Monte Carlo method for open quantum systems
• Quantum Simulation of Dissipative Processes without Reservoir Engineering
• Gaussian trajectory approach to dissipative phase transitions: the case of quadratically driven photonic lattices
• Simulation of single-qubit open quantum systems
• Gaussian Quantum Trajectories for the Variational Simulation of Open Quantum-Optical Systems
• Hardware-efficient quantum algorithm for the simulation of open-system dynamics and thermalisation
• Gutzwiller Monte Carlo approach for a critical dissipative spin model
• Simulating frustrated antiferromagnets with quadratically driven QED cavities
• Short-depth circuits for efficient expectation value estimation

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