Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Systematic and efficient pseudomode method to simulate open quantum systems under a bosonic environment

Lin Zhou, Guangri Jin, Wen Yang

Published Aug 19, 2024• 13 citations
Publisher

Abstract

Using the pseudomode model to simulate open quantum systems is important in quantum physics. Here we report a systematic and efficient pseudomode model based on dissipative, noninteracting harmonic oscillators, capable of accurately simulating any type of environmental spectrum. The dynamical evolution is reduced to a Lindblad master equation with only one dissipation term. A simple procedure to determine the parameters of the pseudomodes is proposed. We evaluate its accuracy by some spin-boson models under different environmental spectra. Our findings consistently exhibit high accuracy. Finally, we extend this pseudomode method to larger systems with more complicated interactions. Our method may have potential applications in quantum information.

DOI
10.1103/physreva.110.022221

Related papers

Pseudomode description of general open quantum system dynamics: non-perturbative master equation for the spin-boson model

Graeme Pleasance, Francesco Petruccione

We outline a non-perturbative approach for simulating the behavior of open quantum systems interacting with a bosonic environment defined by a generalized spectral density function. The method is based on replacing the environment by a set of damped harmonic oscillators - the pseudomodes - thereby forming an enlarged open system whose dynamics is governed by a Markovian master equation. Each pseudomode is connected to one of the poles of the spectral density when analytically continued to the lower-half complex frequency plane. Here, we extend previous results to a completely generic class of open system models, and discuss how our framework can be used as a powerful and versatile tool for analyzing non-Markovian open system dynamics. The effectiveness of the method is demonstrated on the spin-boson model by accurately benchmarking its predictions against numerically exact results.

arXiv:2108.05755•Aug 12, 2021•2 citations

Nonperturbative Treatment of non-Markovian Dynamics of Open Quantum Systems

Dario Tamascelli, Andrea Smirne, S. F. Huelga +1 more

We identify the conditions that guarantee equivalence of the reduced dynamics of an open quantum system (OQS) for two different types of environments-one a continuous bosonic environment leading to a unitary system-environment evolution and the other a discrete-mode bosonic environment resulting in a system-mode (nonunitary) Lindbladian evolution. Assuming initial Gaussian states for the environments, we prove that the two OQS dynamics are equivalent if both the expectation values and two-time correlation functions of the environmental interaction operators are the same at all times for the two configurations. Since the numerical and analytical description of a discrete-mode environment undergoing a Lindbladian evolution is significantly more efficient than that of a continuous bosonic environment in a unitary evolution, our result represents a powerful, nonperturbative tool to describe complex and possibly highly non-Markovian dynamics. As a special application, we recover and generalize the well-known pseudomodes approach to open-system dynamics.

arXiv:1709.03509•Physical Review Letters•Jan 19, 2018•243 citations

Optimized auxiliary oscillators for the simulation of general open quantum systems

F. Mascherpa, Andrea Smirne, Alejandro D. Somoza +5 more

A method for the systematic construction of few-body damped harmonic oscillator networks accurately reproducing the effect of general bosonic environments in open quantum systems is presented. Under the sole assumptions of a Gaussian environment and regardless of the system coupled to it, an algorithm to determine the parameters of an equivalent set of interacting damped oscillators obeying a Markovian quantum master equation is introduced. By choosing a suitable coupling to the system and minimizing an appropriate distance between the two-time correlation function of this effective bath and that of the target environment, the error induced in the reduced dynamics of the system is brought under rigorous control. The interactions among the effective modes provide remarkable flexibility in replicating non-Markovian effects on the system even with a small number of oscillators, and the resulting Lindblad equation for the system and the modes may therefore be integrated at a very reasonable computational cost using standard methods for Markovian problems, even in strongly nonperturbative coupling regimes and at arbitrary temperatures including zero. We apply the method to an exactly solvable problem in order to demonstrate its accuracy, and present two studies based on current research in the context of coherent transport in biological aggregates and organic photovoltaics as more realistic examples of its use and potential; performance and versatility are highlighted, and theoretical and numerical advantages over existing methods, as well as possible future improvements, are discussed.

arXiv:1904.04822•Physical Review A•May 14, 2020•98 citations

Quasi-Lindblad pseudomode theory for open quantum systems

Gunhee Park, Zhen Huang, Yuanran Zhu +3 more

We introduce a new framework to study the dynamics of open quantum systems with linearly coupled Gaussian baths. Our approach replaces the continuous bath with an auxiliary discrete set of pseudomodes with dissipative dynamics, but we further relax the complete positivity requirement in the Lindblad master equation and formulate a quasi-Lindblad pseudomode theory. We show that this quasi-Lindblad pseudomode formulation directly leads to a representation of the bath correlation function in terms of a complex weighted sum of complex exponentials, an expansion that is known to be rapidly convergent in practice and thus leads to a compact set of pseudomodes. The pseudomode representation is not unique and can differ by a gauge choice. When the global dynamics can be simulated exactly, the system dynamics is unique and independent of the specific pseudomode representation. However, the gauge choice may affect the stability of the global dynamics, and we provide an analysis of why and when the global dynamics can retain stability despite losing positivity. We showcase the performance of this formulation across various spectral densities in both bosonic and fermionic problems, finding significant improvements over conventional pseudomode formulations.

arXiv:2408.15529•Physical review. B./Physical review. B•Nov 25, 2024•32 citations

Accurate Two-Time Correlation from a Pseudomode-Based Variational Approach with the Multiple Davydov D1 Density Operator

Yiying Yan, Zhiguo LÜ, Yuguo Su +2 more

The pseudomode framework provides an efficient description of open quantum systems in non-Markovian and nonperturbative coupling regimes by utilizing simple Markovian Lindblad master equations that incorporate a set of damped bosonic pseudomodes. Developing an efficient numerical scheme to solve these equations accurately is highly desirable. In this work, we propose a modified multiple Davydov D1 density operator ansatz and combine it with the Dirac-Frenkel time-dependent variational principle to simulate the dynamics governed by these master equations. We apply this variational method to the spin-boson model, both with and without a periodic external driving field, and compute both single- and two-time expectation values in non-Markovian, strong-coupling regimes. The accuracy of our variational approach is validated by comparing its predictions with results obtained from the small matrix path integral method. We demonstrate that the variational and path-integral approaches are in excellent agreement for both single- and two-time expectations across nondriven and driven cases, spanning both low- and high-temperature regimes. Our results establish the reliability and broad applicability of the pseudomode-based variational approach for calculating two-time correlation functions in open quantum systems.

Journal of Chemical Theory and Computation•Oct 16, 2026•0 citations

Markovian evolution from a novel scheme

Fardin Kheirandish, Zahra Iranshahi, Fatemeh Bakhtiari +1 more

The Markovian dynamics of open quantum many-body systems are typically governed by the Lindblad master equation, yet obtaining the reduced density matrix for bosonic and fermionic systems remains a formidable numerical challenge due to the exponential growth of the Hilbert space. Here, we introduce a computationally efficient framework for constructing the reduced density matrix by modeling the environment as a copy of the primary system with a monotonically decaying coupling that enforces unidirectional energy flow. Our method directly yields exact solutions that rigorously satisfy the Lindblad master equation for both bosonic and fermionic cases, bypassing the need for costly Liouvillian diagonalization. We validate our approach through applications to paradigmatic models, demonstrating accurate reproduction of dissipative dynamics across a broad parameter regime. This work provides a straightforward and powerful tool for simulating Markovian open-system evolution, with immediate applicability to quantum transport and control problems in many-body physics.

quant-pharXiv:2607.13809•Jul 16, 2026•0 citations
Using the pseudomode model to simulate open quantum systems is important in quantum physics. Here we report a systematic and efficient pseudomode model based on dissipative, noninteracting harmonic oscillators, capable of accurately simulating any type of environmental spectrum. The dynamical evolution is reduced to a Lindblad master equation with only one dissipation term. A simple procedure to determine the parameters of the pseudomodes is proposed. We evaluate its accuracy by some spin-boson models under different environmental spectra. Our findings consistently exhibit high accuracy. Finally, we extend this pseudomode method to larger systems with more complicated interactions. Our method may have potential applications in quantum information.
We outline a non-perturbative approach for simulating the behavior of open quantum systems interacting with a bosonic environment defined by a generalized spectral density function. The method is based on replacing the environment by a set of damped harmonic oscillators - the pseudomodes - thereby forming an enlarged open system whose dynamics is governed by a Markovian master equation. Each pseudomode is connected to one of the poles of the spectral density when analytically continued to the lower-half complex frequency plane. Here, we extend previous results to a completely generic class of open system models, and discuss how our framework can be used as a powerful and versatile tool for analyzing non-Markovian open system dynamics. The effectiveness of the method is demonstrated on the spin-boson model by accurately benchmarking its predictions against numerically exact results.
We identify the conditions that guarantee equivalence of the reduced dynamics of an open quantum system (OQS) for two different types of environments-one a continuous bosonic environment leading to a unitary system-environment evolution and the other a discrete-mode bosonic environment resulting in a system-mode (nonunitary) Lindbladian evolution. Assuming initial Gaussian states for the environments, we prove that the two OQS dynamics are equivalent if both the expectation values and two-time correlation functions of the environmental interaction operators are the same at all times for the two configurations. Since the numerical and analytical description of a discrete-mode environment undergoing a Lindbladian evolution is significantly more efficient than that of a continuous bosonic environment in a unitary evolution, our result represents a powerful, nonperturbative tool to describe complex and possibly highly non-Markovian dynamics. As a special application, we recover and generalize the well-known pseudomodes approach to open-system dynamics.
A method for the systematic construction of few-body damped harmonic oscillator networks accurately reproducing the effect of general bosonic environments in open quantum systems is presented. Under the sole assumptions of a Gaussian environment and regardless of the system coupled to it, an algorithm to determine the parameters of an equivalent set of interacting damped oscillators obeying a Markovian quantum master equation is introduced. By choosing a suitable coupling to the system and minimizing an appropriate distance between the two-time correlation function of this effective bath and that of the target environment, the error induced in the reduced dynamics of the system is brought under rigorous control. The interactions among the effective modes provide remarkable flexibility in replicating non-Markovian effects on the system even with a small number of oscillators, and the resulting Lindblad equation for the system and the modes may therefore be integrated at a very reasonable computational cost using standard methods for Markovian problems, even in strongly nonperturbative coupling regimes and at arbitrary temperatures including zero. We apply the method to an exactly solvable problem in order to demonstrate its accuracy, and present two studies based on current research in the context of coherent transport in biological aggregates and organic photovoltaics as more realistic examples of its use and potential; performance and versatility are highlighted, and theoretical and numerical advantages over existing methods, as well as possible future improvements, are discussed.
We introduce a new framework to study the dynamics of open quantum systems with linearly coupled Gaussian baths. Our approach replaces the continuous bath with an auxiliary discrete set of pseudomodes with dissipative dynamics, but we further relax the complete positivity requirement in the Lindblad master equation and formulate a quasi-Lindblad pseudomode theory. We show that this quasi-Lindblad pseudomode formulation directly leads to a representation of the bath correlation function in terms of a complex weighted sum of complex exponentials, an expansion that is known to be rapidly convergent in practice and thus leads to a compact set of pseudomodes. The pseudomode representation is not unique and can differ by a gauge choice. When the global dynamics can be simulated exactly, the system dynamics is unique and independent of the specific pseudomode representation. However, the gauge choice may affect the stability of the global dynamics, and we provide an analysis of why and when the global dynamics can retain stability despite losing positivity. We showcase the performance of this formulation across various spectral densities in both bosonic and fermionic problems, finding significant improvements over conventional pseudomode formulations.
The pseudomode framework provides an efficient description of open quantum systems in non-Markovian and nonperturbative coupling regimes by utilizing simple Markovian Lindblad master equations that incorporate a set of damped bosonic pseudomodes. Developing an efficient numerical scheme to solve these equations accurately is highly desirable. In this work, we propose a modified multiple Davydov D1 density operator ansatz and combine it with the Dirac-Frenkel time-dependent variational principle to simulate the dynamics governed by these master equations. We apply this variational method to the spin-boson model, both with and without a periodic external driving field, and compute both single- and two-time expectation values in non-Markovian, strong-coupling regimes. The accuracy of our variational approach is validated by comparing its predictions with results obtained from the small matrix path integral method. We demonstrate that the variational and path-integral approaches are in excellent agreement for both single- and two-time expectations across nondriven and driven cases, spanning both low- and high-temperature regimes. Our results establish the reliability and broad applicability of the pseudomode-based variational approach for calculating two-time correlation functions in open quantum systems.
The Markovian dynamics of open quantum many-body systems are typically governed by the Lindblad master equation, yet obtaining the reduced density matrix for bosonic and fermionic systems remains a formidable numerical challenge due to the exponential growth of the Hilbert space. Here, we introduce a computationally efficient framework for constructing the reduced density matrix by modeling the environment as a copy of the primary system with a monotonically decaying coupling that enforces unidirectional energy flow. Our method directly yields exact solutions that rigorously satisfy the Lindblad master equation for both bosonic and fermionic cases, bypassing the need for costly Liouvillian diagonalization. We validate our approach through applications to paradigmatic models, demonstrating accurate reproduction of dissipative dynamics across a broad parameter regime. This work provides a straightforward and powerful tool for simulating Markovian open-system evolution, with immediate applicability to quantum transport and control problems in many-body physics.