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:2507.11675

Dynamics Simulation of Arbitrary Non-Hermitian Systems Based on Quantum Monte Carlo

Li, Xiaogang, Kecheng Liu, Qi-Ming Ding

Published Jul 15, 2025• 0 citations
arXivHTMLPDF

Abstract

Non-Hermitian quantum systems exhibit unique properties and hold significant promise for diverse applications, yet their dynamical simulation poses a particular challenge due to intrinsic openness and non-unitary evolution. Here, we introduce a hybrid classical-quantum algorithm based on Quantum Monte Carlo (QMC) for simulating the dynamics of arbitrary time-dependent non-Hermitian systems. Notably, this approach constitutes a natural extension of the quantum imaginary-time evolution (QITE) algorithm. This algorithm combines the advantages of both classical and quantum computation and exhibits good applicability and adaptability, making it promising for simulating arbitrary non-Hermitian systems such as PT-symmetric systems, non-physical processes, and open quantum systems. To validate the algorithm, we applied it to the dynamic simulation of open quantum systems and achieved the desired results.

DOI
10.48550/arxiv.2507.11675

Related papers

Digital Quantum Simulation of Open Quantum Systems Using Quantum Imaginary–Time Evolution

Hirsh Kamakari, Shi-Ning Sun, Mário Motta +1 more

Quantum simulation on emerging quantum hardware is a topic of intense interest.While many studies focus on computing ground-state properties or simulating unitary dynamics of closed systems, open quantum systems are an interesting target of study owing to their ubiquity and rich physical behavior.However, their nonunitary dynamics are also not natural to simulate on digital quantum devices.Here, we report algorithms for the digital quantum simulation of the dynamics of open quantum systems governed by a Lindblad equation using adaptations of the quantum imaginary-time evolution algorithm.We demonstrate the algorithms on IBM Quantum's hardware with simulations of the spontaneous emission of a two-level system and the dissipative transverse field Ising model.Our work advances efforts to simulate the dynamics of open quantum systems on quantum hardware.

arXiv:2104.07823•PRX Quantum•Feb 4, 2022•141 citations

Variational Quantum Simulation of Lindblad Dynamics via Quantum State Diffusion

Jianming Luo, Kaihan Lin, Xing Bao Gao

Quantum simulation of dynamics in open quantum systems is crucial but poses a significant challenge due to the non-Hermitian nature leading to nonunitary evolution and the limited quantum resources on current quantum computers. Here we introduce a variational hybrid quantum-classical algorithm designed for simulating the time evolution governed by the Lindblad master equation. Our approach involves on a stochastic unveiling of the density matrix, transforming the Lindblad equation into a wave function-based quantum state diffusion (QSD) method with the aim of reducing qubit requirements. We then apply variational quantum simulation (VQS) to efficiently capture the nonunitary evolution in QSD. We demonstrate our QSD-VQS algorithm by investigating the quantum dynamics in a two-level system subjected to an amplitude damping channel and a four-level transverse field Ising model within a dissipative environment including time-independent and periodic Hamiltonian cases. The results reveal its promising utility with upcoming hardware in the near future.

The Journal of Physical Chemistry Letters•Mar 22, 2024•21 citations

Variational Quantum Simulation of Open Quantum Dynamics via Non-Markovian Stochastic Schrödinger Equation with Complex Frequency Modes

Yukai Guo, Xing Bao Gao

Simulating non-Markovian open quantum dynamics is crucial for understanding complex quantum systems, yet it poses significant challenges for standard quantum hardware. These challenges stem from the non-Hermitian nature of such dynamics, which results in nonunitary evolution, as well as constraints imposed by limited quantum resources. To address this, we propose a hybrid quantum-classical algorithm designed for simulating dissipative dynamics in systems coupled to non-Markovian environments. Our approach includes formulating a non-Markovian Stochastic Schrödinger equation with complex frequency modes (cNMSSE) where the non-Markovianity is characterized by the mode excitation. We then employ variational quantum simulation to capture the nonunitary evolution within the cNMSSE framework, leading to a substantial reduction in qubit requirements. To demonstrate our approach, we investigated dissiaptive dynamics in the spin-boson model (SBM) and excitation energy transfer processes in both a prototype dimer system and the biologically relevant Fenna-Matthews-Olson (FMO) complex.

Journal of Chemical Theory and Computation•Sep 8, 2025•1 citation

Faster Quantum Monte Carlo Simulation by Random Compilation

John M. Martyn, Joshua Lin, Neill C. Warrington +2 more

Quantum Monte Carlo (QMC) algorithms are among the most powerful classical methods for simulating quantum systems, yet their accuracy is often limited by the systematic errors in the approximations used, such as Trotterization. Here we introduce randomly compiled quantum Monte Carlo (RC-QMC) as a general framework that suppresses these systematic errors by averaging over a family of approximations rather than relying on a single fixed one. This strategy is grounded in the concept of randomized compiling from quantum computing, which suppresses errors by sampling over quantum gates, at essentially no additional computational cost. Consequently, our framework achieves a computational advantage over standard QMC methods when estimating a target state to a desired level of accuracy. We illustrate this advantage on two key Monte Carlo algorithms: (1) path integral quantum Monte Carlo for estimating thermal states, and (2) the quantum trajectories method for simulating open system dynamics. In aggregate, these results represent a cross-fertilization of quantum and classical algorithms, are readily generalizable to other QMC methods, and suggest wider applications in classical simulation.

quant-pharXiv:2609.10486•Sep 10, 2026•0 citations

Recent progress of quantum simulation of non-Hermitian systems

Xue-Er Gao, Dai-Li Li, Zhihang Liu +1 more

Quantum simulation is one of the main contents of quantum information science, aiming to simulate and investigate poorly controllable or unobtainable quantum systems by using controllable quantum systems. Quantum simulation can be implemented in quantum computers, quantum simulators, and small quantum devices. Non-Hermitian systems have aroused research interest increasingly in recent two decades. On one hand, non-Hermitian quantum theories can be seen as the complex extensions of the conventional quantum mechanics, and are closely related to open systems and dissipative systems. On the other hand, both quantum systems and classical systems can be constructed as non-Hermitian systems with novel properties, which can be used to improve the precision of precise measurements. However, a non-Hermitian system is more difficult to simulate than a Hermitian system in that the time evolution of it is no longer unitary. In this review, we introduce recent research progress of quantum simulations of non-Hermitian systems. We mainly introduce theoretical researches to simulate typical non-Hermitian quantum systems by using the linear combinations of unitaries, briefly showing the advantages and limitations of each proposal, and we briefly mention other theoretical simulation methods, such as quantum random walk, space embedded and dilation. Moreover, we briefly introduce the experimental quantum simulations of non-Hermitian systems and novel phenomena in nuclear magnetic resonance, quantum optics and photonics, classical systems, etc. The recent progress of the combinations of quantum simulation and non-Hermitian physics has promoted the development of the non-Hermitian theories, experiments and applications, and expand the scope of application of quantum simulations and quantum computers.

Acta Physica Sinica•Jan 1, 2022•9 citations

Quantum Simulation of Open Quantum Dynamics via Non-Markovian Quantum State Diffusion

Guo, Yukai, Xing Bao Gao

Quantum simulation of non-Markovian open quantum dynamics is essential but challenging for standard quantum computers due to their non-Hermitian nature, leading to non-unitary evolution, and the limitations of available quantum resources. Here we introduce a hybrid quantum-classical algorithm designed for simulating dissipative dynamics in system with non-Markovian environment. Our approach includes formulating a non-Markovian Stochastic Schrödinger equation with complex frequency modes (cNMSSE) where the non-Markovianity is characterized by the mode excitation. Following this, we utilize variational quantum simulation to capture the non-unitary evolution within the cNMSSE framework, leading to a substantial reduction in qubit requirements. To demonstrate our approach, we investigated the spin-boson model and dynamic quantum phase transitions (DQPT) within transverse field Ising model (TFIM). Significantly, our findings reveal the enhanced DQPT in TFIM due to non-Markovian behavior.

arXiv:2404.10655•Apr 16, 2024•2 citations
Non-Hermitian quantum systems exhibit unique properties and hold significant promise for diverse applications, yet their dynamical simulation poses a particular challenge due to intrinsic openness and non-unitary evolution. Here, we introduce a hybrid classical-quantum algorithm based on Quantum Monte Carlo (QMC) for simulating the dynamics of arbitrary time-dependent non-Hermitian systems. Notably, this approach constitutes a natural extension of the quantum imaginary-time evolution (QITE) algorithm. This algorithm combines the advantages of both classical and quantum computation and exhibits good applicability and adaptability, making it promising for simulating arbitrary non-Hermitian systems such as PT-symmetric systems, non-physical processes, and open quantum systems. To validate the algorithm, we applied it to the dynamic simulation of open quantum systems and achieved the desired results.
Quantum simulation on emerging quantum hardware is a topic of intense interest.While many studies focus on computing ground-state properties or simulating unitary dynamics of closed systems, open quantum systems are an interesting target of study owing to their ubiquity and rich physical behavior.However, their nonunitary dynamics are also not natural to simulate on digital quantum devices.Here, we report algorithms for the digital quantum simulation of the dynamics of open quantum systems governed by a Lindblad equation using adaptations of the quantum imaginary-time evolution algorithm.We demonstrate the algorithms on IBM Quantum's hardware with simulations of the spontaneous emission of a two-level system and the dissipative transverse field Ising model.Our work advances efforts to simulate the dynamics of open quantum systems on quantum hardware.
Quantum simulation of dynamics in open quantum systems is crucial but poses a significant challenge due to the non-Hermitian nature leading to nonunitary evolution and the limited quantum resources on current quantum computers. Here we introduce a variational hybrid quantum-classical algorithm designed for simulating the time evolution governed by the Lindblad master equation. Our approach involves on a stochastic unveiling of the density matrix, transforming the Lindblad equation into a wave function-based quantum state diffusion (QSD) method with the aim of reducing qubit requirements. We then apply variational quantum simulation (VQS) to efficiently capture the nonunitary evolution in QSD. We demonstrate our QSD-VQS algorithm by investigating the quantum dynamics in a two-level system subjected to an amplitude damping channel and a four-level transverse field Ising model within a dissipative environment including time-independent and periodic Hamiltonian cases. The results reveal its promising utility with upcoming hardware in the near future.
Simulating non-Markovian open quantum dynamics is crucial for understanding complex quantum systems, yet it poses significant challenges for standard quantum hardware. These challenges stem from the non-Hermitian nature of such dynamics, which results in nonunitary evolution, as well as constraints imposed by limited quantum resources. To address this, we propose a hybrid quantum-classical algorithm designed for simulating dissipative dynamics in systems coupled to non-Markovian environments. Our approach includes formulating a non-Markovian Stochastic Schrödinger equation with complex frequency modes (cNMSSE) where the non-Markovianity is characterized by the mode excitation. We then employ variational quantum simulation to capture the nonunitary evolution within the cNMSSE framework, leading to a substantial reduction in qubit requirements. To demonstrate our approach, we investigated dissiaptive dynamics in the spin-boson model (SBM) and excitation energy transfer processes in both a prototype dimer system and the biologically relevant Fenna-Matthews-Olson (FMO) complex.
Quantum Monte Carlo (QMC) algorithms are among the most powerful classical methods for simulating quantum systems, yet their accuracy is often limited by the systematic errors in the approximations used, such as Trotterization. Here we introduce randomly compiled quantum Monte Carlo (RC-QMC) as a general framework that suppresses these systematic errors by averaging over a family of approximations rather than relying on a single fixed one. This strategy is grounded in the concept of randomized compiling from quantum computing, which suppresses errors by sampling over quantum gates, at essentially no additional computational cost. Consequently, our framework achieves a computational advantage over standard QMC methods when estimating a target state to a desired level of accuracy. We illustrate this advantage on two key Monte Carlo algorithms: (1) path integral quantum Monte Carlo for estimating thermal states, and (2) the quantum trajectories method for simulating open system dynamics. In aggregate, these results represent a cross-fertilization of quantum and classical algorithms, are readily generalizable to other QMC methods, and suggest wider applications in classical simulation.
Quantum simulation is one of the main contents of quantum information science, aiming to simulate and investigate poorly controllable or unobtainable quantum systems by using controllable quantum systems. Quantum simulation can be implemented in quantum computers, quantum simulators, and small quantum devices. Non-Hermitian systems have aroused research interest increasingly in recent two decades. On one hand, non-Hermitian quantum theories can be seen as the complex extensions of the conventional quantum mechanics, and are closely related to open systems and dissipative systems. On the other hand, both quantum systems and classical systems can be constructed as non-Hermitian systems with novel properties, which can be used to improve the precision of precise measurements. However, a non-Hermitian system is more difficult to simulate than a Hermitian system in that the time evolution of it is no longer unitary. In this review, we introduce recent research progress of quantum simulations of non-Hermitian systems. We mainly introduce theoretical researches to simulate typical non-Hermitian quantum systems by using the linear combinations of unitaries, briefly showing the advantages and limitations of each proposal, and we briefly mention other theoretical simulation methods, such as quantum random walk, space embedded and dilation. Moreover, we briefly introduce the experimental quantum simulations of non-Hermitian systems and novel phenomena in nuclear magnetic resonance, quantum optics and photonics, classical systems, etc. The recent progress of the combinations of quantum simulation and non-Hermitian physics has promoted the development of the non-Hermitian theories, experiments and applications, and expand the scope of application of quantum simulations and quantum computers.
Quantum simulation of non-Markovian open quantum dynamics is essential but challenging for standard quantum computers due to their non-Hermitian nature, leading to non-unitary evolution, and the limitations of available quantum resources. Here we introduce a hybrid quantum-classical algorithm designed for simulating dissipative dynamics in system with non-Markovian environment. Our approach includes formulating a non-Markovian Stochastic Schrödinger equation with complex frequency modes (cNMSSE) where the non-Markovianity is characterized by the mode excitation. Following this, we utilize variational quantum simulation to capture the non-unitary evolution within the cNMSSE framework, leading to a substantial reduction in qubit requirements. To demonstrate our approach, we investigated the spin-boson model and dynamic quantum phase transitions (DQPT) within transverse field Ising model (TFIM). Significantly, our findings reveal the enhanced DQPT in TFIM due to non-Markovian behavior.