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:2311.17622 · Advanced Quantum Technologies

Non‐Markovianity Benefits Quantum Dynamics Simulation

Y. Chen, Shi‐Xin Zhang, Shengyu Zhang

Published Nov 20, 2025• 1 citation
arXivHTMLPDF

Abstract

ABSTRACT Quantum dynamics simulation on analog quantum simulators and digital quantum computers has emerged as a powerful and promising tool for understanding complex non‐equilibrium physics. However, the impact of quantum noise on quantum dynamics simulation, particularly non‐Markovian noise with memory effects, has remained elusive. In this work, we discover unexpected benefits of non‐Markovianity of quantum noise in quantum dynamics simulation. We demonstrate that non‐Markovian noise with memory effects and temporal correlations can significantly improve the accuracy of quantum dynamics simulation on quantum computers compared to the Markovian noise of the same strength. Through theoretical analysis and extensive numerical experiments, we showcase the positive effects and nontrivial physics induced by non‐Markovian noise in various dynamics simulation scenarios, including decoherence dynamics of idle qubits, intriguing non‐equilibrium dynamics observed in symmetry protected topological phases and many‐body localization phases. Our findings shed light on the importance of considering non‐Markovianity in quantum simulation and open up new avenues for investigating quantum phenomena and designing more efficient and robust quantum technologies.

DOI
10.1002/qute.202500405

Related papers

How rare are Markovian quantum dynamics?

Charlotte Bäcker, Nick Maryshchak, Walter T. Strunz

A profound understanding of decoherence and dissipation in quantum dynamics is crucial for the realistic modeling of the evolution of quantum systems. In open quantum dynamics one distinguishes between a memoryless, so-called Markovian evolution and dynamics incorporating memory effects, termed non-Markovian. In this work we study how prevalent memory effects are in the set of all such dynamics. We thus investigate how often a Markovian description is applicable. This question is approached by investigating randomly generated two-step qubit dynamics with respect to different concepts and witnesses of non-Markovianity. We observe that almost all dynamics are non-Markovian, and only a small (yet finite) fraction is Markovian. Furthermore, we study how this proportion changes when considering certain subclasses such as lower rank or mixed-unitary dynamics. Importantly, our results shed light on the relative ratios of -- and interrelations between -- the sets of dynamics that are non-Markovian with respect to different criteria. Finally, we investigate the fraction of dynamics in which the memory effects are necessarily of quantum nature and establish a connection between two recently developed concepts that characterize the quantumness of memory in non-Markovian dynamics.

quant-pharXiv:2606.24511•Jun 24, 2026•0 citations

Investigating Non-Markovian Effects on Quantum Dynamics in Open Quantum Systems

Mariia Ivanchenko, Peter Walters, Fei Wang

The reduced description of the quantum dynamic processes in the condensed phase environment leads to the equation of motion with a memory kernel. Such a memory effect, termed non-Markovianity, presents more complex dynamics compared to its memoryless or Markovian counterpart, and many chemical systems have been demonstrated through numerical simulations to exhibit non-Markovian quantum dynamics. Explicitly how the memory impacts the dynamic process remains largely unexplored. In this work, we focus on ways to separate the non-Markovian contributions from the dynamics and study the non-Markovian effects. Specifically, we developed a rigorous procedure for mapping the exact non-Markovian quantum propagator to the Lindblad form. Consequently, it allows us to extract the negative decay rate from the Lindbladian that is the signature of the non-Markovianity. By including or excluding the negative rate in the time evolution, we can decisively pinpoint the influence of non-Markovianity on the system's properties such as coherence, entanglement, and equilibrium state distribution. The understanding of such memory effects on the dynamic process suggests the possibility of leveraging non-Markovianity for quantum control.

Journal of Chemical Theory and Computation•Jun 12, 2025•5 citations

Low-depth simulation of non-Markovianity under quantum hardware noise

Diana A. Chisholm

Simulating open quantum systems on digital quantum computers typically relies on the use of auxiliary qubits, resulting in overheads of noisy multi-qubit gates, that severely limit execution on near-term hardware. In this work, we explore the simulation of non-Markovian dynamics as well as memory channels leveraging the method of trajectory mixing, valid for mixed unitary channels. This allows to drastically reduce circuit depth, trading entangling gates for a statistical mixture of independent, pure state trajectories. Using a realistic noise model calibrated to modern quantum processors, we show the benefits of this approach, yielding higher state fidelity and better preservation of quantum correlations. This shows the possibility of simulating long-time non-Markovian evolutions with low noise and limited resources.

quant-pharXiv:2607.05519•Jul 8, 2026•0 citations

Foundations and measures of quantum non-Markovianity

Heinz‐Peter Breuer

The basic features of the dynamics of open quantum systems, such as the dissipation of energy, the decay of coherences, the relaxation to an equilibrium or non-equilibrium stationary state, and the transport of excitations in complex structures are of central importance in many applications of quantum mechanics. The theoretical description, analysis and control of non-Markovian quantum processes play an important role in this context. While in a Markovian process an open system irretrievably loses information to its surroundings, non-Markovian processes feature a flow of information from the environment back to the open system, which implies the presence of memory effects and represents the key property of non-Markovian quantum behavior. Here, we review recent ideas developing a general mathematical definition for non-Markoviantiy in the quantum regime and a measure for the degree of memory effects in the dynamics of open systems which are based on the exchange of information between system and environment. We further study the dynamical effects induced by the presence of system-environment correlations in the total initial state and design suitable methods to detect such correlations through local measurements on the open system.

arXiv:1206.5346•Journal of Physics B Atomic Molecular and Optical Physics•Jul 30, 2012•223 citations

Impact of Temporally Correlated Dephasing Noise on the Fidelity of the 2-Qubit Deutsch-Jozsa Algorithm

Ghosh, Souvik

Understanding the influence of realistic noise on quantum algorithms is paramount for the advancement of quantum computation. While often modeled as Markovian, environmental noise in quantum systems frequently exhibits temporal correlations, leading to non-Markovian dynamics that can significantly alter algorithmic performance. This paper investigates the impact of temporally correlated dephasing noise, modeled by the Ornstein-Uhlenbeck (OU) process, on the fidelity of the 2-qubit Deutsch-Jozsa algorithm. We perform numerical simulations using Qiskit, systematically varying the noise strength ($σ_{\text{OU}}$) and correlation time ($τ_c$) of the OU process. Our results demonstrate that the algorithm's fidelity exhibits a non-monotonic dependence on $τ_c$, particularly at higher noise strengths, with certain intermediate correlation times proving more detrimental than others. We find that a standard Markovian dephasing model, matched to the single-step error variance of the OU process, accurately predicts fidelity only in the limit of very short correlation times. For longer correlation times, the Markovian approximation often overestimates the algorithm's fidelity, failing to capture the complex error dynamics introduced by the noise memory. These findings highlight the necessity of incorporating non-Markovian characteristics for accurate performance assessment of quantum algorithms on near-term devices and underscore the limitations of simpler, memoryless noise models.

arXiv:2506.05509•Jun 5, 2025•0 citations

Tripartite Quantum Correlations under Power‐Law and Random Telegraph Noises: Collective Effects of Markovian and Non‐Markovian Classical Fields

Atta Ur Rahman, Saeed Haddadi, Mohammad Reza Pourkarimi

Abstract The collective effects of Markovian and non‐Markovian classical fields on the dynamics of entanglement, coherence, and quantum state mixing in a three‐qubit mixed entangled state are examined. Three independent local fields are considered to be influenced by the decoherence effects of two different mixed noisy models: Markovian maximized and non‐Markovian maximized local random configurations. Power‐law noise characterizes two classical environments in the first case, whereas random telegraph noise governs the third. Random telegraph noise rules two classical environments in the latter example, whereas power‐law noise governs the third. In classical fields, non‐Markovian effects are more robust and have a stronger character than Markovian effects, yet both are driven by relevant noises. Non‐Markovianity vanishes at the upper bound of the Markovian noise parameters. Markovian effects are found to be vulnerable to the environments non‐Markovianity and longer memory features. The strength of Markovianity and non‐Markovianity is only moderately affected by the type of environment, but noise parameter optimization has a significant impact. Initial and final limits are provided for the restriction and relaxation in Markovianity and non‐Markovianity of the classical fields for the actual deployment of non‐local protocols.

Annalen der Physik•Mar 17, 2022•27 citations
ABSTRACT Quantum dynamics simulation on analog quantum simulators and digital quantum computers has emerged as a powerful and promising tool for understanding complex non‐equilibrium physics. However, the impact of quantum noise on quantum dynamics simulation, particularly non‐Markovian noise with memory effects, has remained elusive. In this work, we discover unexpected benefits of non‐Markovianity of quantum noise in quantum dynamics simulation. We demonstrate that non‐Markovian noise with memory effects and temporal correlations can significantly improve the accuracy of quantum dynamics simulation on quantum computers compared to the Markovian noise of the same strength. Through theoretical analysis and extensive numerical experiments, we showcase the positive effects and nontrivial physics induced by non‐Markovian noise in various dynamics simulation scenarios, including decoherence dynamics of idle qubits, intriguing non‐equilibrium dynamics observed in symmetry protected topological phases and many‐body localization phases. Our findings shed light on the importance of considering non‐Markovianity in quantum simulation and open up new avenues for investigating quantum phenomena and designing more efficient and robust quantum technologies.
A profound understanding of decoherence and dissipation in quantum dynamics is crucial for the realistic modeling of the evolution of quantum systems. In open quantum dynamics one distinguishes between a memoryless, so-called Markovian evolution and dynamics incorporating memory effects, termed non-Markovian. In this work we study how prevalent memory effects are in the set of all such dynamics. We thus investigate how often a Markovian description is applicable. This question is approached by investigating randomly generated two-step qubit dynamics with respect to different concepts and witnesses of non-Markovianity. We observe that almost all dynamics are non-Markovian, and only a small (yet finite) fraction is Markovian. Furthermore, we study how this proportion changes when considering certain subclasses such as lower rank or mixed-unitary dynamics. Importantly, our results shed light on the relative ratios of -- and interrelations between -- the sets of dynamics that are non-Markovian with respect to different criteria. Finally, we investigate the fraction of dynamics in which the memory effects are necessarily of quantum nature and establish a connection between two recently developed concepts that characterize the quantumness of memory in non-Markovian dynamics.
The reduced description of the quantum dynamic processes in the condensed phase environment leads to the equation of motion with a memory kernel. Such a memory effect, termed non-Markovianity, presents more complex dynamics compared to its memoryless or Markovian counterpart, and many chemical systems have been demonstrated through numerical simulations to exhibit non-Markovian quantum dynamics. Explicitly how the memory impacts the dynamic process remains largely unexplored. In this work, we focus on ways to separate the non-Markovian contributions from the dynamics and study the non-Markovian effects. Specifically, we developed a rigorous procedure for mapping the exact non-Markovian quantum propagator to the Lindblad form. Consequently, it allows us to extract the negative decay rate from the Lindbladian that is the signature of the non-Markovianity. By including or excluding the negative rate in the time evolution, we can decisively pinpoint the influence of non-Markovianity on the system's properties such as coherence, entanglement, and equilibrium state distribution. The understanding of such memory effects on the dynamic process suggests the possibility of leveraging non-Markovianity for quantum control.
Simulating open quantum systems on digital quantum computers typically relies on the use of auxiliary qubits, resulting in overheads of noisy multi-qubit gates, that severely limit execution on near-term hardware. In this work, we explore the simulation of non-Markovian dynamics as well as memory channels leveraging the method of trajectory mixing, valid for mixed unitary channels. This allows to drastically reduce circuit depth, trading entangling gates for a statistical mixture of independent, pure state trajectories. Using a realistic noise model calibrated to modern quantum processors, we show the benefits of this approach, yielding higher state fidelity and better preservation of quantum correlations. This shows the possibility of simulating long-time non-Markovian evolutions with low noise and limited resources.
The basic features of the dynamics of open quantum systems, such as the dissipation of energy, the decay of coherences, the relaxation to an equilibrium or non-equilibrium stationary state, and the transport of excitations in complex structures are of central importance in many applications of quantum mechanics. The theoretical description, analysis and control of non-Markovian quantum processes play an important role in this context. While in a Markovian process an open system irretrievably loses information to its surroundings, non-Markovian processes feature a flow of information from the environment back to the open system, which implies the presence of memory effects and represents the key property of non-Markovian quantum behavior. Here, we review recent ideas developing a general mathematical definition for non-Markoviantiy in the quantum regime and a measure for the degree of memory effects in the dynamics of open systems which are based on the exchange of information between system and environment. We further study the dynamical effects induced by the presence of system-environment correlations in the total initial state and design suitable methods to detect such correlations through local measurements on the open system.
Understanding the influence of realistic noise on quantum algorithms is paramount for the advancement of quantum computation. While often modeled as Markovian, environmental noise in quantum systems frequently exhibits temporal correlations, leading to non-Markovian dynamics that can significantly alter algorithmic performance. This paper investigates the impact of temporally correlated dephasing noise, modeled by the Ornstein-Uhlenbeck (OU) process, on the fidelity of the 2-qubit Deutsch-Jozsa algorithm. We perform numerical simulations using Qiskit, systematically varying the noise strength (σOUσ_{\text{OU}}σOU​) and correlation time (τcτ_cτc​) of the OU process. Our results demonstrate that the algorithm's fidelity exhibits a non-monotonic dependence on τcτ_cτc​, particularly at higher noise strengths, with certain intermediate correlation times proving more detrimental than others. We find that a standard Markovian dephasing model, matched to the single-step error variance of the OU process, accurately predicts fidelity only in the limit of very short correlation times. For longer correlation times, the Markovian approximation often overestimates the algorithm's fidelity, failing to capture the complex error dynamics introduced by the noise memory. These findings highlight the necessity of incorporating non-Markovian characteristics for accurate performance assessment of quantum algorithms on near-term devices and underscore the limitations of simpler, memoryless noise models.
Abstract The collective effects of Markovian and non‐Markovian classical fields on the dynamics of entanglement, coherence, and quantum state mixing in a three‐qubit mixed entangled state are examined. Three independent local fields are considered to be influenced by the decoherence effects of two different mixed noisy models: Markovian maximized and non‐Markovian maximized local random configurations. Power‐law noise characterizes two classical environments in the first case, whereas random telegraph noise governs the third. Random telegraph noise rules two classical environments in the latter example, whereas power‐law noise governs the third. In classical fields, non‐Markovian effects are more robust and have a stronger character than Markovian effects, yet both are driven by relevant noises. Non‐Markovianity vanishes at the upper bound of the Markovian noise parameters. Markovian effects are found to be vulnerable to the environments non‐Markovianity and longer memory features. The strength of Markovianity and non‐Markovianity is only moderately affected by the type of environment, but noise parameter optimization has a significant impact. Initial and final limits are provided for the restriction and relaxation in Markovianity and non‐Markovianity of the classical fields for the actual deployment of non‐local protocols.