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

arXiv:2408.03543 · Physical Review A

Classical-quantum correspondence in noise-based dissipative systems

Jiarui Zeng, Guohao Xu, Weijie Huang, Yao Yao

Published Dec 26, 2024• 3 citations
arXivHTMLPDF

Abstract

We investigate the correspondence between classical noise and quantum environments. Although it is known that classical noise can be mapped to quantum environments for pure dephasing and infinite-temperature dissipation processes, we show how finite-temperature dissipation can be also described using classical noise by introducing auxiliary systems and conservation. Taking a two-level system as an example, we construct the so-called central spin model with its couplings fluctuating with the classical noise and then acquire its statistical-average dynamics which captures the dissipation beyond infinite temperature. By adjusting the number of auxiliary systems and their initial states, the noise-based model reproduces both Markovian and non-Markovian evolution. We also find that different quantities of the two-level system are governed by different model parameters, indicating that the constructed model is an effective simulator for specific observables rather than an equivalent form of a realistic open system. In addition, the model is also applicable to investigate topical mechanisms of open systems, e.g., negative temperatures and asymmetric equidistant quenches.

DOI
10.1103/physreva.110.062219

Related papers

Quantifying environment nonclassicality in dissipative open quantum dynamics

Adrián A. Budini

Open quantum systems are inherently coupled to their environments, which in turn also obey quantum dynamical rules. Restricting ourselves to dissipative dynamics, here we propose a measure that quantifies how far the action of an environment on a system departs from the influence of classical noise fluctuations. It is based on the lack of commutativity between the initial reservoir state and the total system-environment Hamiltonian. Independently of the nature of the dissipative system evolution, Markovian or non-Markovian, the measure can be written in terms of the dual propagator that defines the evolution of system operators. The physical meaning and properties of the proposed definition are discussed in detail and also characterized through different paradigmatic dissipative Markovian and non-Markovian open quantum dynamics.

arXiv:2305.16136•Physical Review A•Oct 6, 2023•4 citations

Open quantum dynamics theory for a complex subenvironment system with a quantum thermostat: Application to a spin heat bath

Kiyoto Nakamura, Yoshitaka Tanimura

Complex environments, such as molecular matrices and biological material, play a fundamental role in many important dynamic processes in condensed phases. Because it is extremely difficult to conduct full quantum dynamics simulations on such environments due to their many degrees of freedom, here, we treat in detail the environment only around the main system of interest (the subenvironment), while the other degrees of freedom needed to maintain the equilibrium temperature are described by a simple harmonic bath, which we call a quantum thermostat. The noise generated by the subenvironment is spatially non-local and non-Gaussian and cannot be characterized by the fluctuation-dissipation theorem. We describe this model by simulating the dynamics of a two-level system (TLS) that interacts with a subenvironment consisting of a one-dimensional XXZ spin chain. The hierarchical Schrödinger equations of motion are employed to describe the quantum thermostat, allowing for time-irreversible simulations of the dynamics at arbitrary temperature. To see the effects of a quantum phase transition of the subenvironment, we investigate the decoherence and relaxation processes of the TLS at zero and finite temperatures for various values of the spin anisotropy. We observed the decoherence of the TLS at finite temperature even when the anisotropy of the XXZ model is enormous. We also found that the population-relaxation dynamics of the TLS changed in a complex manner with the change in the anisotropy and the ferromagnetic or antiferromagnetic orders of spins.

arXiv:2111.13277•The Journal of Chemical Physics•Nov 30, 2021•9 citations

Exact solutions of non-Markovian dissipative Ising models

Mohammad Maghrebi

Applications of quantum devices and simulators require an accurate understanding of their dynamics as well as the effects of environmental noise. While some sources of noise can be modeled as Markovian dissipation, coupling to resonators or vibrational modes often produces non-Markovian dynamics as well, making it difficult to characterize the system, particularly for interacting many-body systems. Here, we identify a broad class of exactly solvable many-body quantum systems with both non-Markovian dynamics and Markovian dissipation. We consider a prototypical model of spins coupled to lossy bosonic modes that mediate Ising-type interactions. We exclude a transverse field but allow local spin dissipation that need not commute with the interactions, including dephasing, relaxation, pumping, and even processes that generate coherences. Using an exact stochastic representation, we decouple the many-body dynamics into the evolution of individual spins, yielding exact spin observables and correlations without adiabatically eliminating the bosons. In the Markovian limit, our solutions describe Ising models with correlated dephasing and nonreciprocal interactions. An example of spin squeezing shows that both the achievable squeezing and its optimal preparation time depend strongly on the interplay between non-Markovian dynamics and Markovian dissipation.

quant-pharXiv:2610.12546•Oct 12, 2026•0 citations

STOCHASTIC NOISE APPROACH TO NON-MARKOVIAN DECOHERENCE IN CONTINUOUS VARIABLE OPEN QUANTUM SYSTEMS

Jacopo Trapani

In this PHD thesis, I address the study of the evolution of quantum correlations of continuous variable systems interacting with classical environments, portrayed by classical stochastic fields. In particular, the first goal is individuating the working regimes where a full quantum description of the system-environment interaction may be simulated with a stochastic approach. As a paradigmatic example, I consider quantum harmonic oscillators subject to phase diffusion and dissipation decoherence. My results show that the stochastic noise may take over the full quantum description of Markovian dephasing channels, while a stochastic approach to dissipation only works at a high temperature in the early stage of the dynamics. The second goal consists in better exploring the connection between the dynamics of correlations of the system, non-Markovianity and backflow of information. In many situations non-Markovianity cannot be proved but only revealed by means of appropriate witnesses, usually associated to backflow of information. My results show that stochastic phase diffusing and stochastic dissipative environments lead to non-Markovian dynamics, but their non-Markovianity stays unwitnessed unless revivals of correlations as nonclassicality, entanglement or discord are detected. This suggests that non-Markovianity sets the natural framework for revivals of correlations, but the true resource to obtain revivals is the backflow of information. The third goal consists in showing that effects of local or global noise on a bipartite system may easily be distinguished by means of standard laboratory techniques. Indeed, my results show that homodyne-detection-based schemes may discriminate the effects of a global stochastic noise affecting two probes from local perturbation, using as states of the probe ?lab-friendly? states.

•Jan 19, 2017•4 citations

Finite-Bath Open Quantum Systems: Exact Dynamics

Devvrat Tiwari, Subhashish Banerjee

In this work, we introduce a method for deriving exact master equations from the dynamical map for finite open quantum systems coupled to (in)finite reservoirs, using the principle of minimal dissipation. The exact dynamics of the central spin model, which models a finite-bath open quantum system, is developed for two interaction types: Heisenberg and stochastic pure-dephasing interactions. The Heisenberg interaction yields a novel phase-covariant quantum channel in the strong-coupling regime, offering a new platform for studying a range of quantum information protocols. The stochastic pure-dephasing interaction provides the microscopic derivation of the paradigmatic non-Markovian random telegraph noise (RTN) channel, establishing its quantum foundation and offering insight into stochastic couplings. We derive the closed-form master equations for both models. As a demonstration, we explore the thermodynamic performance of these systems as quantum batteries. A direct relationship between quantum heat current and charging power is revealed, and RTN quantum batteries are shown to have advantages in charge storage.

quant-pharXiv:2511.07180•The Journal of Chemical Physics•Nov 11, 2025•0 citations

An ensemble variational quantum algorithm for non-Markovian quantum dynamics

Peter Walters, Joachim Tsakanikas, Fei Wang

Many physical and chemical processes in a condensed phase environment exhibit non-Markovian quantum dynamics. As such simulations are challenging on classical computers, we developed a variational quantum algorithm that is capable of simulating non-Markovian dynamics on noisy intermediate-scale quantum (NISQ) devices. We used a quantum system linearly coupled to its harmonic bath as the model Hamiltonian. The non-Markovianity is captured by introducing auxiliary variables from the bath trajectories. With Monte Carlo sampling of the bath degrees of freedom, finite temperature dynamics is produced. We validated the algorithm on a simulator and demonstrated its performance on an IBM quantum device. The framework developed naturally adapts to any anharmonic bath with non-linear coupling to the system, and is also well suited for simulating spin chain dynamics in a dissipative environment.

Physical Chemistry Chemical Physics•Jan 1, 2024•4 citations
We investigate the correspondence between classical noise and quantum environments. Although it is known that classical noise can be mapped to quantum environments for pure dephasing and infinite-temperature dissipation processes, we show how finite-temperature dissipation can be also described using classical noise by introducing auxiliary systems and conservation. Taking a two-level system as an example, we construct the so-called central spin model with its couplings fluctuating with the classical noise and then acquire its statistical-average dynamics which captures the dissipation beyond infinite temperature. By adjusting the number of auxiliary systems and their initial states, the noise-based model reproduces both Markovian and non-Markovian evolution. We also find that different quantities of the two-level system are governed by different model parameters, indicating that the constructed model is an effective simulator for specific observables rather than an equivalent form of a realistic open system. In addition, the model is also applicable to investigate topical mechanisms of open systems, e.g., negative temperatures and asymmetric equidistant quenches.
Open quantum systems are inherently coupled to their environments, which in turn also obey quantum dynamical rules. Restricting ourselves to dissipative dynamics, here we propose a measure that quantifies how far the action of an environment on a system departs from the influence of classical noise fluctuations. It is based on the lack of commutativity between the initial reservoir state and the total system-environment Hamiltonian. Independently of the nature of the dissipative system evolution, Markovian or non-Markovian, the measure can be written in terms of the dual propagator that defines the evolution of system operators. The physical meaning and properties of the proposed definition are discussed in detail and also characterized through different paradigmatic dissipative Markovian and non-Markovian open quantum dynamics.
Complex environments, such as molecular matrices and biological material, play a fundamental role in many important dynamic processes in condensed phases. Because it is extremely difficult to conduct full quantum dynamics simulations on such environments due to their many degrees of freedom, here, we treat in detail the environment only around the main system of interest (the subenvironment), while the other degrees of freedom needed to maintain the equilibrium temperature are described by a simple harmonic bath, which we call a quantum thermostat. The noise generated by the subenvironment is spatially non-local and non-Gaussian and cannot be characterized by the fluctuation-dissipation theorem. We describe this model by simulating the dynamics of a two-level system (TLS) that interacts with a subenvironment consisting of a one-dimensional XXZ spin chain. The hierarchical Schrödinger equations of motion are employed to describe the quantum thermostat, allowing for time-irreversible simulations of the dynamics at arbitrary temperature. To see the effects of a quantum phase transition of the subenvironment, we investigate the decoherence and relaxation processes of the TLS at zero and finite temperatures for various values of the spin anisotropy. We observed the decoherence of the TLS at finite temperature even when the anisotropy of the XXZ model is enormous. We also found that the population-relaxation dynamics of the TLS changed in a complex manner with the change in the anisotropy and the ferromagnetic or antiferromagnetic orders of spins.
Applications of quantum devices and simulators require an accurate understanding of their dynamics as well as the effects of environmental noise. While some sources of noise can be modeled as Markovian dissipation, coupling to resonators or vibrational modes often produces non-Markovian dynamics as well, making it difficult to characterize the system, particularly for interacting many-body systems. Here, we identify a broad class of exactly solvable many-body quantum systems with both non-Markovian dynamics and Markovian dissipation. We consider a prototypical model of spins coupled to lossy bosonic modes that mediate Ising-type interactions. We exclude a transverse field but allow local spin dissipation that need not commute with the interactions, including dephasing, relaxation, pumping, and even processes that generate coherences. Using an exact stochastic representation, we decouple the many-body dynamics into the evolution of individual spins, yielding exact spin observables and correlations without adiabatically eliminating the bosons. In the Markovian limit, our solutions describe Ising models with correlated dephasing and nonreciprocal interactions. An example of spin squeezing shows that both the achievable squeezing and its optimal preparation time depend strongly on the interplay between non-Markovian dynamics and Markovian dissipation.
In this PHD thesis, I address the study of the evolution of quantum correlations of continuous variable systems interacting with classical environments, portrayed by classical stochastic fields. In particular, the first goal is individuating the working regimes where a full quantum description of the system-environment interaction may be simulated with a stochastic approach. As a paradigmatic example, I consider quantum harmonic oscillators subject to phase diffusion and dissipation decoherence. My results show that the stochastic noise may take over the full quantum description of Markovian dephasing channels, while a stochastic approach to dissipation only works at a high temperature in the early stage of the dynamics. The second goal consists in better exploring the connection between the dynamics of correlations of the system, non-Markovianity and backflow of information. In many situations non-Markovianity cannot be proved but only revealed by means of appropriate witnesses, usually associated to backflow of information. My results show that stochastic phase diffusing and stochastic dissipative environments lead to non-Markovian dynamics, but their non-Markovianity stays unwitnessed unless revivals of correlations as nonclassicality, entanglement or discord are detected. This suggests that non-Markovianity sets the natural framework for revivals of correlations, but the true resource to obtain revivals is the backflow of information. The third goal consists in showing that effects of local or global noise on a bipartite system may easily be distinguished by means of standard laboratory techniques. Indeed, my results show that homodyne-detection-based schemes may discriminate the effects of a global stochastic noise affecting two probes from local perturbation, using as states of the probe ?lab-friendly? states.
In this work, we introduce a method for deriving exact master equations from the dynamical map for finite open quantum systems coupled to (in)finite reservoirs, using the principle of minimal dissipation. The exact dynamics of the central spin model, which models a finite-bath open quantum system, is developed for two interaction types: Heisenberg and stochastic pure-dephasing interactions. The Heisenberg interaction yields a novel phase-covariant quantum channel in the strong-coupling regime, offering a new platform for studying a range of quantum information protocols. The stochastic pure-dephasing interaction provides the microscopic derivation of the paradigmatic non-Markovian random telegraph noise (RTN) channel, establishing its quantum foundation and offering insight into stochastic couplings. We derive the closed-form master equations for both models. As a demonstration, we explore the thermodynamic performance of these systems as quantum batteries. A direct relationship between quantum heat current and charging power is revealed, and RTN quantum batteries are shown to have advantages in charge storage.
Many physical and chemical processes in a condensed phase environment exhibit non-Markovian quantum dynamics. As such simulations are challenging on classical computers, we developed a variational quantum algorithm that is capable of simulating non-Markovian dynamics on noisy intermediate-scale quantum (NISQ) devices. We used a quantum system linearly coupled to its harmonic bath as the model Hamiltonian. The non-Markovianity is captured by introducing auxiliary variables from the bath trajectories. With Monte Carlo sampling of the bath degrees of freedom, finite temperature dynamics is produced. We validated the algorithm on a simulator and demonstrated its performance on an IBM quantum device. The framework developed naturally adapts to any anharmonic bath with non-linear coupling to the system, and is also well suited for simulating spin chain dynamics in a dissipative environment.