Simulating Bosonic Baths with Error Bars

Abstract

We derive rigorous truncation-error bounds for the spin-boson model and its generalizations to arbitrary quantum systems interacting with bosonic baths. For the numerical simulation of such baths the truncation of both, the number of modes and the local Hilbert-space dimensions is necessary. We derive super-exponential Lieb--Robinson-type bounds on the error when restricting the bath to finitely-many modes and show how the error introduced by truncating the local Hilbert spaces may be efficiently monitored numerically. In this way we give error bounds for approximating the infinite system by a finite-dimensional one. As a consequence, numerical simulations such as the time-evolving density with orthogonal polynomials algorithm (TEDOPA) now allow for the fully certified treatment of the system-environment interaction.

13 pages, 3 figures

References in corpus (9)

• Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials
• Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model
• Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Universal Markovian reduction of Brownian particle dynamics
• Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
• Computational Methodologies and Physical Insights into Electronic Energy Transfer in Photosynthetic Light-Harvesting Complexes
• Quantum dynamics in photonic crystals
• Lieb-Robinson Bounds for the Toda Lattice

Cited by in corpus (46)

• Efficient simulation of finite-temperature open quantum systems
• Resource-efficient digital quantum simulation of $d$-level systems for photonic, vibrational, and spin-$s$ Hamiltonians
• Energy transfer in structured and unstructured environments: master equations beyond the Born-Markov approximations
• Fermionic reaction coordinates and their application to an autonomous Maxwell demon in the strong coupling regime
• Optimized auxiliary oscillators for the simulation of general open quantum systems
• Efficient simulation of non-Markovian system-environment interaction
• Dissipation-assisted matrix product factorization
• Locality and digital quantum simulation of power-law interactions
• Provably accurate simulation of gauge theories and bosonic systems
• Simulating generic spin-boson models with matrix product states
• Digital quantum simulation of many-body non-Markovian dynamics
• Tightening the Lieb-Robinson Bound in Locally-Interacting Systems
• Near- and long-term quantum algorithmic approaches for vibrational spectroscopy
• Open systems with error bounds: spin boson model with spectral density variations
• Periodically refreshed baths to simulate open quantum many-body dynamics
• Efficient simulation of open quantum systems coupled to a fermionic bath
• Quantum probing beyond pure dephasing
• Lieb-Robinson bound and almost-linear light-cone in interacting boson systems
• Phase-dependent exciton transport and energy harvesting from thermal environments
• Non-perturbative treatment of giant atoms using chain transformations
• Dynamical error bounds for continuum discretisation via Gauss quadrature rules, -- a Lieb-Robinson bound approach
• Steady state quantum transport through an anharmonic oscillator strongly coupled to two heat reservoirs
• Quasi-Lindblad pseudomode theory for open quantum systems
• Quantum thermodynamics with fast driving and strong coupling via the mesoscopic leads approach
• Fingerprint and universal Markovian closure of structured bosonic environments
• The reaction coordinate mapping in quantum thermodynamics
• Unveiling non-Markovian spacetime signalling in open quantum systems with long-range tensor network dynamics
• MPSDynamics.jl: Tensor network simulations for finite-temperature (non-Markovian) open quantum system dynamics
• Exponential clustering of bipartite quantum entanglement at arbitrary temperatures
• Convergence guarantees for discrete mode approximations to non-Markovian quantum baths
• Effective light cone and digital quantum simulation of interacting bosons
• Excitation dynamics in chain-mapped environments
• Periodically refreshed quantum thermal machines
• Digital quantum simulation of non-perturbative dynamics of open systems with orthogonal polynomials
• Coupled Lindblad pseudomode theory for simulating open quantum systems
• Bounding the finite-size error of quantum many-body dynamics simulations
• Extracting Dynamical Maps of Non-Markovian Open Quantum Systems
• Spectral Density Modulation and Universal Markovian Closure of Fermionic Environments
• Efficient construction of tensor-network representations of many-body Gaussian states
• Making Quantum Collision Models Exact
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
• Efficient tensor network simulation of multi-emitter non-Markovian systems
• Influence of non-adiabatic effects on linear absorption spectra in the condensed phase: Methylene blue
• Separation of relaxation timescales via strong system-bath coupling: Dissipative three-level system as a case study
• Chain-mapping methods for relativistic light-matter interactions
• A posteriori error estimates for the Lindblad master equation