Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems

Abstract

Non-Markovian open quantum systems represent the most general dynamics when the quantum system is coupled with a bath environment. The quantum dynamics arising from many important applications are non-Markovian. Although for special cases, such as Hamiltonian evolution and Lindblad evolution, quantum simulation algorithms have been extensively studied, efficient quantum simulations for the dynamics of non-Markovian open quantum systems remain underexplored. The most immediate obstacle for studying such systems is the lack of a universal succinct description of their dynamics. In this work, we fulfill the gap of studying such dynamics by 1) providing a succinct representation of the dynamics of non-Markovian open quantum systems with quantifiable error, and 2) developing an efficient quantum algorithm for simulating such dynamics with cost $O(t\mathrm{polylog}(t/\epsilon ))$ for evolution time $t$ and precision $\epsilon$. Our derivation of the succinct representation is based on stochastic Schrödinger equations, which could lead to new alternatives to deal with open quantum systems as well.

arXiv comment39 pages, no figures. To appear in Communications in Mathematical Physics

References in corpus (35)

• Decoherence Free Subspaces for Quantum Computation
• Non-Markovian dynamics in open quantum systems
• Hamiltonian Simulation by Qubitization
• Optimal Hamiltonian Simulation by Quantum Signal Processing
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Efficient quantum algorithms for simulating sparse Hamiltonians
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
• Hamiltonian simulation with nearly optimal dependence on all parameters
• Open system dynamics with non-Markovian quantum trajectories
• Non-Markovian quantum processes: complete framework and efficient characterisation
• The non-Markovian stochastic Schrodinger equation for open systems
• Non-Markovian quantum dynamics: local versus non-local
• Hierarchy of stochastic pure states for open quantum system dynamics
• Exponential improvement in precision for simulating sparse Hamiltonians
• Observation of non-Markovian micro-mechanical Brownian motion
• Enhanced quantum entanglement in the non-Markovian dynamics of biomolecular excitons
• A dissipative quantum Church-Turing theorem
• Observation of non-Markovian dynamics of a single quantum dot in a micropillar cavity
• Current induced light emission and light induced current in molecular tunneling junctions
• From Completely Positive Maps to the Quantum Markovian Semigroup Master Equation
• Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators
• Quantifying non-Markovianity of continuous variable Gaussian dynamical maps
• Linear quantum state diffusion for non-Markovian open quantum systems
• Analytic Representations of Bath Correlation Functions for Ohmic and Superohmic Spectral Densities Using Simple Poles
• Generalized Quantum Master Equations In and Out of Equilibrium: When Can One Win?
• Approximate but Accurate Quantum Dynamics from the Mori Formalism: I. Nonequilibrium Dynamics
• Digital quantum simulation of many-body non-Markovian dynamics
• Efficient construction of generalized master equation memory kernels for multi-state systems from nonadiabatic quantum-classical dynamics
• Exact dynamics of quantum correlations of two qubits coupled to bosonic baths
• Approximate but accurate quantum dynamics from the Mori formalism: II. Equilibrium correlation functions
• Qubit Decoherence and Non-Markovian Dynamics at Low Temperatures via an Effective Spin-Boson Model
• Spin-boson model as a simulator of non-Markovian multiphoton Jaynes-Cummings models
• Lindblad equation and its semi-classical limit of the Anderson-Holstein model

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