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:2610.29372

Quantum Simulation of Non-Markovian Open Quantum Systems via Low-Rank Kernel Compression and Coupling Dilution

Hengzhun Chen, Zhenning Cai

quant-phSubmitted Oct 21, 2026• Announced Oct 22, 2026• 0 citations
arXivHTMLPDF

Abstract

We present an error-controlled framework for the quantum simulation of non-Markovian open-system dynamics in Gaussian environments. For a system coupled linearly to a Gaussian environment with zero mean, the bath's influence on the reduced dynamics is completely determined by its two-time correlation kernel. This allows us to replace the microscopic environment with an equivalent bath that has the same kernel. On a finite simulation interval, a rank-$N$ approximation of the kernel yields an effective bath of $N$ bosonic modes with time-dependent couplings to the system. To encode these modes in qubits, we first truncate each mode to its lowest $d$ occupation levels. When stronger couplings lead to large occupations, we introduce coupling dilution, which replaces each mode with several more weakly coupled copies while preserving the bath correlation kernel. This distributes excitations across more modes and trades additional modes for smaller local dimensions. We derive explicit reduced-state error bounds and establish polynomial circuit width and depth in simulation time and inverse accuracy under stated spectral-decay and coupling-regularity assumptions, provided elementary unitaries admit polynomial-cost implementations.

Related papers

Ancilla-train quantum algorithm for simulating non-Markovian open quantum systems

Hans Michael Christensen, Johannes Agerskov, Frederik Nathan

We present a quantum algorithm for simulating open quantum systems coupled to Gaussian environments valid for any configuration and coupling strength. The algorithm is applicable to problems with strongly coupled, or non-Markovian, environments; problems with multiple environments out of mutual equilibrium; and problems with time-dependent Hamiltonians. We show that the algorithm can reproduce the true dynamics of such problems at arbitrary accuracy and, for a broad range of problems, only adds a minor resource cost relative to Trotterized time evolution; the cost is low-degree polynomial in the inverse target accuracy. The algorithm is based on the insight that any Gaussian environment can be represented as a train of ancillary qubits that sequentially interact with the system through a time-local coupling, given by the convolution square root of the bath correlation function; this is a secondary result of our work. In numerical simulations of a spin-boson model, we find accurate simulations can be achieved with moderate ( 10 1 – 10 3 ) ancilla counts in the intermediate to strong-coupling regimes. Our results open up applications of quantum computers for efficient simulation of nonequilibrium and open quantum systems.

arXiv:2509.12717•Physical Review A•Aug 19, 2026•0 citations

Non-Markovian dynamics of a two-level system in a bosonic bath and a Gaussian fluctuating environment with finite correlation time

V. A. Mikhailov, Nikolay V. Troshkin

The character of evolution of an open quantum system is often encoded in the correlation function of the environment or, equivalently, in the spectral density function of the interaction. When the environment is heterogeneous, e.g., consists of several independent subenvironments with different spectral functions, one of the subenvironments can be considered auxiliary and used to control decoherence of the open quantum system in the remaining part of the environment. The control can be realized, for example, by adjusting the character of interaction with the subenvironment via suitable parameters of its spectral density. We investigate non-Markovian evolution of a two-level system (qubit) under influence of three independent decoherence channels: two of them have classical nature and originate from interaction with a stochastic field, and the third is a quantum channel formed by interaction with a bosonic bath. By modifying spectral densities of the channels, we study their impact on steady states of the two-level system, evolution of its density matrix, and the equilibrium emission spectra. Additionally, we investigate the impact of the rotation-wave approximation applied to the bath channel on accuracy of the results.

arXiv:2005.12897•Physical Review A•Jan 13, 2021•6 citations

Convergence Guarantees for Discrete Mode Approximations to Non-Markovian Quantum Baths

Rahul Trivedi, Daniel Malz, J. Ignacio Cirac

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.

arXiv:2107.07196•Physical Review Letters•Dec 15, 2021•20 citations

Using the Environment to Understand non-Markovian Open Quantum Systems

Dominic Gribben, Aidan Strathearn, Gerald E. Fux +2 more

Tracing out the environmental degrees of freedom is a necessary procedure when simulating open quantum systems. While being an essential step in deriving a tractable master equation it represents a loss of information. In situations where there is strong interplay between the system and environmental degrees of freedom this loss makes understanding the dynamics challenging. These dynamics, when viewed in isolation, have no time-local description: they are non-Markovian and memory effects induce complex features that are difficult to interpret. To address this problem, we here show how to use system correlations, calculated by any method, to infer any correlation function of a Gaussian environment, so long as the coupling between system and environment is linear. This not only allows reconstruction of the full dynamics of both system and environment, but also opens avenues into studying the effect of a system on its environment. In order to obtain accurate bath dynamics, we exploit a numerically exact approach to simulating the system dynamics, which is based on the construction and contraction of a tensor network that represents the process tensor of this open quantum system. Using this we are able to find any system correlation function exactly. To demonstrate the applicability of our method we show how heat moves between different modes of a bosonic bath when coupled to a two-level system that is subject to an off-resonant drive.

arXiv:2106.04212•Quantum•Oct 25, 2022•41 citations

Quantum Fast Forwarding of Non-Markovian Quantum Dynamics

Avin Seneviratne, Peter Walters, Fei Wang

In this work, we present a quantum algorithm for simulating non-Markovian quantum dynamics based on the Feynman-Vernon influence functional formalism, which provides an exact description of the dynamics of a quantum system linearly coupled to a harmonic bath. In condensed-phase environments, the bath correlation functions typically decay over time, allowing them to be truncated beyond a finite time scale and enabling an iterative propagation scheme. We implement the finite-memory propagator using a fast-forwarding algorithm that achieves constant circuit depth with respect to the number of propagation steps, while the nonunitary matrices are realized on quantum circuits using unitary dilation. We further exploit the structure of the unitary dilation to show that the additional circuit complexity introduced by the dilation scales polynomially with the number of dilation ancilla qubits, while the dominant computational cost arises from the implementation of the underlying 1-dilation. The algorithm is compared with classical benchmark calculations for the spin-boson model and shows close agreement. Together, these developments establish a quantum-circuit framework for fast forwarding non-Markovian dynamics and identify the principal computational bottlenecks that must be overcome to achieve quantum advantage.

The Journal of Physical Chemistry Letters•Oct 12, 2026•0 citations

Provably Efficient Long-Time Exponential Decompositions of Non-Markovian Gaussian Baths

Zhen Huang, Zhiyan Ding, Ke Wang +3 more

Gaussian baths are widely used to model non-Markovian environments, yet the cost of accurate simulation at long times remains poorly understood, especially when spectral densities exhibit nonanalytic behavior as in a range of realistic models. We rigorously bound the complexity of representing bath correlation functions on a time interval $[0,T]$ by sums of complex exponentials, as employed in recent variants of pseudomode and hierarchical equations of motion methods. These bounds make explicit the dependence on the maximal simulation time $T$, inverse temperature $β$, and the type and strength of singularities in an effective spectral density. For a broad class of spectral densities, the required number of exponentials is bounded independently of $T$, achieving time-uniform complexity. The $T$-dependence emerges only as polylogarithmic factors for spectral densities with strong singularities, such as step discontinuities and inverse power-law divergences. The temperature dependence is mild for bosonic environments and disappears entirely for fermionic environments. Thus, the true bottleneck for long-time simulation is not the simulation duration itself, but rather the presence of sharp nonanalytic features in the bath spectrum. Our results are instructive both for long-time simulation of non-Markovian open quantum systems, as well as for Markovian embeddings of classical generalized Langevin equations with memory kernels.

quant-pharXiv:2603.25708•Physical Review Research•Mar 27, 2026•0 citations
We present an error-controlled framework for the quantum simulation of non-Markovian open-system dynamics in Gaussian environments. For a system coupled linearly to a Gaussian environment with zero mean, the bath's influence on the reduced dynamics is completely determined by its two-time correlation kernel. This allows us to replace the microscopic environment with an equivalent bath that has the same kernel. On a finite simulation interval, a rank-NNN approximation of the kernel yields an effective bath of NNN bosonic modes with time-dependent couplings to the system. To encode these modes in qubits, we first truncate each mode to its lowest ddd occupation levels. When stronger couplings lead to large occupations, we introduce coupling dilution, which replaces each mode with several more weakly coupled copies while preserving the bath correlation kernel. This distributes excitations across more modes and trades additional modes for smaller local dimensions. We derive explicit reduced-state error bounds and establish polynomial circuit width and depth in simulation time and inverse accuracy under stated spectral-decay and coupling-regularity assumptions, provided elementary unitaries admit polynomial-cost implementations.
We present a quantum algorithm for simulating open quantum systems coupled to Gaussian environments valid for any configuration and coupling strength. The algorithm is applicable to problems with strongly coupled, or non-Markovian, environments; problems with multiple environments out of mutual equilibrium; and problems with time-dependent Hamiltonians. We show that the algorithm can reproduce the true dynamics of such problems at arbitrary accuracy and, for a broad range of problems, only adds a minor resource cost relative to Trotterized time evolution; the cost is low-degree polynomial in the inverse target accuracy. The algorithm is based on the insight that any Gaussian environment can be represented as a train of ancillary qubits that sequentially interact with the system through a time-local coupling, given by the convolution square root of the bath correlation function; this is a secondary result of our work. In numerical simulations of a spin-boson model, we find accurate simulations can be achieved with moderate ( 10 1 – 10 3 ) ancilla counts in the intermediate to strong-coupling regimes. Our results open up applications of quantum computers for efficient simulation of nonequilibrium and open quantum systems.
The character of evolution of an open quantum system is often encoded in the correlation function of the environment or, equivalently, in the spectral density function of the interaction. When the environment is heterogeneous, e.g., consists of several independent subenvironments with different spectral functions, one of the subenvironments can be considered auxiliary and used to control decoherence of the open quantum system in the remaining part of the environment. The control can be realized, for example, by adjusting the character of interaction with the subenvironment via suitable parameters of its spectral density. We investigate non-Markovian evolution of a two-level system (qubit) under influence of three independent decoherence channels: two of them have classical nature and originate from interaction with a stochastic field, and the third is a quantum channel formed by interaction with a bosonic bath. By modifying spectral densities of the channels, we study their impact on steady states of the two-level system, evolution of its density matrix, and the equilibrium emission spectra. Additionally, we investigate the impact of the rotation-wave approximation applied to the bath channel on accuracy of the results.
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.
Tracing out the environmental degrees of freedom is a necessary procedure when simulating open quantum systems. While being an essential step in deriving a tractable master equation it represents a loss of information. In situations where there is strong interplay between the system and environmental degrees of freedom this loss makes understanding the dynamics challenging. These dynamics, when viewed in isolation, have no time-local description: they are non-Markovian and memory effects induce complex features that are difficult to interpret. To address this problem, we here show how to use system correlations, calculated by any method, to infer any correlation function of a Gaussian environment, so long as the coupling between system and environment is linear. This not only allows reconstruction of the full dynamics of both system and environment, but also opens avenues into studying the effect of a system on its environment. In order to obtain accurate bath dynamics, we exploit a numerically exact approach to simulating the system dynamics, which is based on the construction and contraction of a tensor network that represents the process tensor of this open quantum system. Using this we are able to find any system correlation function exactly. To demonstrate the applicability of our method we show how heat moves between different modes of a bosonic bath when coupled to a two-level system that is subject to an off-resonant drive.
In this work, we present a quantum algorithm for simulating non-Markovian quantum dynamics based on the Feynman-Vernon influence functional formalism, which provides an exact description of the dynamics of a quantum system linearly coupled to a harmonic bath. In condensed-phase environments, the bath correlation functions typically decay over time, allowing them to be truncated beyond a finite time scale and enabling an iterative propagation scheme. We implement the finite-memory propagator using a fast-forwarding algorithm that achieves constant circuit depth with respect to the number of propagation steps, while the nonunitary matrices are realized on quantum circuits using unitary dilation. We further exploit the structure of the unitary dilation to show that the additional circuit complexity introduced by the dilation scales polynomially with the number of dilation ancilla qubits, while the dominant computational cost arises from the implementation of the underlying 1-dilation. The algorithm is compared with classical benchmark calculations for the spin-boson model and shows close agreement. Together, these developments establish a quantum-circuit framework for fast forwarding non-Markovian dynamics and identify the principal computational bottlenecks that must be overcome to achieve quantum advantage.
Gaussian baths are widely used to model non-Markovian environments, yet the cost of accurate simulation at long times remains poorly understood, especially when spectral densities exhibit nonanalytic behavior as in a range of realistic models. We rigorously bound the complexity of representing bath correlation functions on a time interval [0,T][0,T][0,T] by sums of complex exponentials, as employed in recent variants of pseudomode and hierarchical equations of motion methods. These bounds make explicit the dependence on the maximal simulation time TTT, inverse temperature βββ, and the type and strength of singularities in an effective spectral density. For a broad class of spectral densities, the required number of exponentials is bounded independently of TTT, achieving time-uniform complexity. The TTT-dependence emerges only as polylogarithmic factors for spectral densities with strong singularities, such as step discontinuities and inverse power-law divergences. The temperature dependence is mild for bosonic environments and disappears entirely for fermionic environments. Thus, the true bottleneck for long-time simulation is not the simulation duration itself, but rather the presence of sharp nonanalytic features in the bath spectrum. Our results are instructive both for long-time simulation of non-Markovian open quantum systems, as well as for Markovian embeddings of classical generalized Langevin equations with memory kernels.