Convergence guarantees for discrete mode approximations to non-Markovian quantum baths

Abstract

Non-Markovian effects are important in modeling the behavior of open quantum systems arising in solid-state physics, quantum optics as well as in study of biological and chemical systems. The non-Markovian environment is often approximated by discrete bosonic modes, thus mapping it to a Lindbladian or Hamiltonian simulation problem. While systematic constructions of such modes have been previously proposed, the resulting approximation lacks rigorous and general convergence guarantees. In this letter, we show that under some physically motivated assumptions on the system-environment interaction, the finite-time dynamics of the non-Markovian open quantum system computed with a sufficiently large number of modes is guaranteed to converge to the true result. Furthermore, we show that this approximation error typically falls off polynomially with the number of modes. Our results lend rigor to classical and quantum algorithms for approximating non-Markovian dynamics.

References in corpus (14)

• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials
• Input-Output Formalism For Few-Photon Transport in One-Dimensional Nanophotonic Waveguides Coupled to a Qubit
• Non-perturbative treatment of non-Markovian dynamics of open quantum systems
• Atomic three-body loss as a dynamical three-body interaction
• Matrix Product States for dynamical simulation of infinite chains
• Exact master equations for the non-Markovian decay of a qubit
• Engineering and harnessing giant atoms in high-dimensional baths: a cold atoms' implementation
• Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level system
• Time-convolutionless master equation for mesoscopic electron-phonon systems
• Open systems with error bounds: spin boson model with spectral density variations
• Theory of non-Markovian decay of a cascade atom in high-Q cavities and photonic band-gap materials
• Extension of the Nakajima-Zwanzig approach to multitime correlation functions of open systems
• Linear-algebraic bath transformation for simulating complex open quantum systems

Cited by in corpus (18)

• Taming Quantum Noise for Efficient Low Temperature Simulations of Open Quantum Systems
• Few-mode Field Quantization for Multiple Emitters
• Non-Hermitian Pseudomodes for Strongly Coupled Open Quantum Systems: Unravelings, Correlations and Thermodynamics
• Non-perturbative treatment of giant atoms using chain transformations
• Quasi-Lindblad pseudomode theory for open quantum systems
• Certifying multi-mode light-matter interaction in lossy resonators
• Master equations and quantum trajectories for squeezed wave packets
• Modeling the unphysical pseudomode model with physical ensembles: simulation, mitigation, and restructuring of non-Markovian quantum noise
• Fixing detailed balance in ancilla-based dissipative state engineering
• Pseudomode treatment of strong-coupling quantum thermodynamics
• A tensor network approach to sensing quantum light-matter interactions
• Coupled Lindblad pseudomode theory for simulating open quantum systems
• Efficient tensor network simulation of multi-emitter non-Markovian systems
• Multimode-cavity picture of non-Markovian waveguide QED
• Chain-mapping methods for relativistic light-matter interactions
• Effective Hamiltonian approach to the exact dynamics of open system by complex discretization approximation for environment
• Subtleties in the pseudomodes formalism
• Position-Resolved Resonance Quantization for Lossy Cavities