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

IEEE Conference on Decision and Control (CDC)

Data-driven spectral analysis of quantum spin networks with limited access using Hankel dynamic mode decomposition

Yuzuru Kato, Hiroya Nakao

Published Dec 6, 2022• 1 citation
Publisher

Abstract

Dynamic mode decomposition (DMD) is an equation-free, data-driven method for the prediction and control of complex dynamical systems. A DMD method for data-driven quantum control was proposed recently and numerically demonstrated in a single spin system where time series of a complete orthonormal set of Hamiltonian is available [1]. In quantum spin networks, it is generally difficult to access all spins but only a small set of spins is practically accessible. In this paper, we formulate a Hankel-DMD method for open quantum systems and extend the applicability of the DMD framework to quantum spin networks with limited access. We demonstrate that Hankel DMD can precisely evaluate the eigenvalues and decompose the dynamics into the respective oscillatory eigenmodes from the observed data. In particular, it can reveal the decoherence-free dynamics in spin networks possessing eigenvalues on the imaginary axis.

DOI
10.1109/cdc51059.2022.9993116

Related papers

Dynamical Mode Decomposition for Infinite-Dimensional Open Quantum Systems; Liouvillian Spectral Analysis and Parameter Estimation

Yuzuru Kato, Hiroya Nakao

Dynamic mode decomposition (DMD) is a data-driven method for the estimation, prediction, and control of complex dynamical systems, which has gained much attention in the fields of nonlinear dynamics and fluid mechanics. A DMD method for quantum spin systems, described by a linear dynamical system of a finite-dimensional set of observables, has been proposed recently. In this study, we propose two DMD methods applicable to infinite-dimensional open quantum systems, which use time-series data obtained by quantum state tomography. First, we propose a kernel DMD method for a data-driven spectral analysis of the Liouville superoperator. Second, we propose a method for the parameter estimation of the Liouville superoperator, which incorporates prior knowledge of the model structure into DMD. The proposed methods can accurately reconstruct the system dynamics and show that DMD frameworks can be applicable to infinite-dimensional open quantum systems.

IEEE Conference on Decision and Control (CDC)•Dec 13, 2023•0 citations

Predicting rate kernels via dynamic mode decomposition

Wei Liu, Zi‐Hao Chen, Yu Su +2 more

Simulating dynamics of open quantum systems is sometimes a significant challenge, despite the availability of various exact or approximate methods. Particularly when dealing with complex systems, the huge computational cost will largely limit the applicability of these methods. In this work, we investigate the usage of dynamic mode decomposition (DMD) to evaluate the rate kernels in quantum rate processes. DMD is a data-driven model reduction technique that characterizes the rate kernels using snapshots collected from a small time window, allowing us to predict the long-term behaviors with only a limited number of samples. Our investigations show that whether the external field is involved or not, the DMD can give accurate prediction of the result compared with the traditional propagations, and simultaneously reduce the required computational cost.

arXiv:2308.01635•The Journal of Chemical Physics•Oct 12, 2023•11 citations

Analyzing and predicting non-equilibrium many-body dynamics via dynamic mode decomposition

Jia Yin, Yang‐Hao Chan, Felipe H. da Jornada +3 more

Simulating the dynamics of a nonequilibrium quantum many-body system by computing the two-time Green's function associated with such a system is computationally challenging. However, we are often interested in the time-diagonal of such a Green's function or time-dependent physical observables that are functions of one time. In this paper, we discuss the possibility of using dynamic mode decomposition (DMD), a data-driven model order reduction technique, to characterize one-time observables associated with the nonequilibrium dynamics using snapshots computed within a small time window. The DMD method allows us to efficiently predict long time dynamics from a limited number of trajectory samples. We demonstrate the effectiveness of DMD on a model two-band system. We show that, in the equilibrium limit, the DMD analysis yields results that are consistent with those produced from a linear response analysis. In the nonequilibrium case, the extrapolated dynamics produced by DMD is more accurate than a special Fourier extrapolation scheme presented in this paper. We point out a potential pitfall of the standard DMD method caused by insufficient spatial/momentum resolution of the discretization scheme. We show how this problem can be overcome by using a variant of the DMD method known as higher order DMD.

arXiv:2107.09635•Journal of Computational Physics•Jan 16, 2023•22 citations

Learning Quantum Operator Dynamics from Short-Time Data

Jinyang Li, Satoshi Iso, Shunji Matsuura +2 more

Real-time dynamics of quantum observables provide direct access to excitation spectra and correlation functions in quantum many-body systems, but currently available quantum devices are limited to short evolution times due to decoherence. We propose a neural ordinary differential equation (Neural ODE) framework with a physics-driven neural network to reconstruct long-time operator dynamics from short-time quantum data. By expanding observables in the Pauli basis and exploiting locality and symmetry constraints, the operator evolution is reduced to a tractable set of coefficients whose dynamics are learned from the measurement data. Applied to the Ising spin chain with mixed fields, the operator learning method accurately extrapolates its long-time correlation function and resolves its excitation spectrum. We validate the framework by collecting short-time data from IBM's superconducting quantum processor and successfully reconstruct the Fourier spectrum of an $N=8$ Ising spin chain with 5 times enhanced precision. Our results demonstrate a scalable and data-efficient strategy for extracting dynamical and spectral information from practical quantum hardware.

quant-pharXiv:2603.14699•Mar 17, 2026•0 citations

Quantum Dynamic Mode Decomposition Algorithm for High-Dimensional Time Series Analysis

Cheng Xue, Zhaoyun Chen, Tai‐Ping Sun +6 more

The dynamic mode decomposition (DMD) algorithm is a widely used factorization and dimensionality reduction technique in time series analysis. When analyzing high-dimensional time series, the DMD algorithm requires extremely large amounts of computational power. To accelerate the DMD algorithm, we propose a quantum-classical hybrid algorithm that we call the quantum dynamic mode decomposition (QDMD) algorithm. Given a time series X ∈ R n × ( m + 1) with n ≫ m , the QDMD algorithm first executes quantum singular value decomposition on a matrix related to X and obtains a quantum state containing the main singular values and singular vectors of the decomposed matrix, then performs a low-sampling-frequency process on the obtained quantum state and computes the low-dimensional projection of the DMD operator through the sampling results. Finally, the algorithm computes the DMD eigenvalues and prepares the amplitude-encoding states of the DMD modes using the obtained classical information and X . Considering the main variables, the complexity of the QDMD algorithm is O ~ M m polylog n / ϵ , where M = O ~ m 3 / ϵ 2 denotes the number of samples. Compared with the classical DMD algorithm, which has complexity O ~ n m 2 log 1 / ϵ , the QDMD algorithm provides an exponential acceleration of n , at the cost of greater dependence on M and ϵ . We test the effects of M on the QDMD algorithm in the specific application scenarios of data denoising, scene background extraction, and fluid dynamics analysis. We determined that the QDMD algorithm requires only a small number of samples M in specific applications, further demonstrating the quantum advantage of the QDMD algorithm in high-dimensional data analysis.

Intelligent Computing•Jan 1, 2023•5 citations

Spectral analysis of the Koopman operator as a framework for recovering Hamiltonian parameters in open quantum systems

Jorge E. Pérez-García, Carlos Colchero, Julio C. Gutiérrez-Vega

Accurate identification of Hamiltonian parameters is essential for modeling and controlling open quantum systems. In this work, we demonstrate that the multichannel Hankel alternative view of Koopman (mHAVOK) algorithm is a robust and reliable spectral data-driven method for retrieving Hamiltonian parameters from the evolution of first-moment observables in open quantum systems. The method relies on the discrete spectrum of the Koopman operator to obtain these parameters, which are computed using the mHAVOK algorithm; a theoretical connection to this affirmation is presented. The method is tested on noiseless quadratures of an open two-dimensional quantum harmonic oscillator and shown to retrieve oscillation frequencies, damping rates, nonlinear Kerr shifts, the qubit-photon coupling strength of a Jaynes-Cummings interaction, and the modulated frequency of a time-dependent Hamiltonian. The majority of the recovered parameters remained within 5% of their actual values. Compared with Fourier and matrix-pencil estimators, our approach yields lower errors for dynamics with strong dissipation. Overall, these findings suggest that Koopman operator theory provides a practical framework for studying quantum dynamical systems.

quant-pharXiv:2511.23470•Physical Review A•Dec 1, 2025•0 citations
Dynamic mode decomposition (DMD) is an equation-free, data-driven method for the prediction and control of complex dynamical systems. A DMD method for data-driven quantum control was proposed recently and numerically demonstrated in a single spin system where time series of a complete orthonormal set of Hamiltonian is available [1]. In quantum spin networks, it is generally difficult to access all spins but only a small set of spins is practically accessible. In this paper, we formulate a Hankel-DMD method for open quantum systems and extend the applicability of the DMD framework to quantum spin networks with limited access. We demonstrate that Hankel DMD can precisely evaluate the eigenvalues and decompose the dynamics into the respective oscillatory eigenmodes from the observed data. In particular, it can reveal the decoherence-free dynamics in spin networks possessing eigenvalues on the imaginary axis.
Dynamic mode decomposition (DMD) is a data-driven method for the estimation, prediction, and control of complex dynamical systems, which has gained much attention in the fields of nonlinear dynamics and fluid mechanics. A DMD method for quantum spin systems, described by a linear dynamical system of a finite-dimensional set of observables, has been proposed recently. In this study, we propose two DMD methods applicable to infinite-dimensional open quantum systems, which use time-series data obtained by quantum state tomography. First, we propose a kernel DMD method for a data-driven spectral analysis of the Liouville superoperator. Second, we propose a method for the parameter estimation of the Liouville superoperator, which incorporates prior knowledge of the model structure into DMD. The proposed methods can accurately reconstruct the system dynamics and show that DMD frameworks can be applicable to infinite-dimensional open quantum systems.
Simulating dynamics of open quantum systems is sometimes a significant challenge, despite the availability of various exact or approximate methods. Particularly when dealing with complex systems, the huge computational cost will largely limit the applicability of these methods. In this work, we investigate the usage of dynamic mode decomposition (DMD) to evaluate the rate kernels in quantum rate processes. DMD is a data-driven model reduction technique that characterizes the rate kernels using snapshots collected from a small time window, allowing us to predict the long-term behaviors with only a limited number of samples. Our investigations show that whether the external field is involved or not, the DMD can give accurate prediction of the result compared with the traditional propagations, and simultaneously reduce the required computational cost.
Simulating the dynamics of a nonequilibrium quantum many-body system by computing the two-time Green's function associated with such a system is computationally challenging. However, we are often interested in the time-diagonal of such a Green's function or time-dependent physical observables that are functions of one time. In this paper, we discuss the possibility of using dynamic mode decomposition (DMD), a data-driven model order reduction technique, to characterize one-time observables associated with the nonequilibrium dynamics using snapshots computed within a small time window. The DMD method allows us to efficiently predict long time dynamics from a limited number of trajectory samples. We demonstrate the effectiveness of DMD on a model two-band system. We show that, in the equilibrium limit, the DMD analysis yields results that are consistent with those produced from a linear response analysis. In the nonequilibrium case, the extrapolated dynamics produced by DMD is more accurate than a special Fourier extrapolation scheme presented in this paper. We point out a potential pitfall of the standard DMD method caused by insufficient spatial/momentum resolution of the discretization scheme. We show how this problem can be overcome by using a variant of the DMD method known as higher order DMD.
Real-time dynamics of quantum observables provide direct access to excitation spectra and correlation functions in quantum many-body systems, but currently available quantum devices are limited to short evolution times due to decoherence. We propose a neural ordinary differential equation (Neural ODE) framework with a physics-driven neural network to reconstruct long-time operator dynamics from short-time quantum data. By expanding observables in the Pauli basis and exploiting locality and symmetry constraints, the operator evolution is reduced to a tractable set of coefficients whose dynamics are learned from the measurement data. Applied to the Ising spin chain with mixed fields, the operator learning method accurately extrapolates its long-time correlation function and resolves its excitation spectrum. We validate the framework by collecting short-time data from IBM's superconducting quantum processor and successfully reconstruct the Fourier spectrum of an N=8N=8N=8 Ising spin chain with 5 times enhanced precision. Our results demonstrate a scalable and data-efficient strategy for extracting dynamical and spectral information from practical quantum hardware.
The dynamic mode decomposition (DMD) algorithm is a widely used factorization and dimensionality reduction technique in time series analysis. When analyzing high-dimensional time series, the DMD algorithm requires extremely large amounts of computational power. To accelerate the DMD algorithm, we propose a quantum-classical hybrid algorithm that we call the quantum dynamic mode decomposition (QDMD) algorithm. Given a time series X ∈ R n × ( m + 1) with n ≫ m , the QDMD algorithm first executes quantum singular value decomposition on a matrix related to X and obtains a quantum state containing the main singular values and singular vectors of the decomposed matrix, then performs a low-sampling-frequency process on the obtained quantum state and computes the low-dimensional projection of the DMD operator through the sampling results. Finally, the algorithm computes the DMD eigenvalues and prepares the amplitude-encoding states of the DMD modes using the obtained classical information and X . Considering the main variables, the complexity of the QDMD algorithm is O ~ M m polylog n / ϵ , where M = O ~ m 3 / ϵ 2 denotes the number of samples. Compared with the classical DMD algorithm, which has complexity O ~ n m 2 log 1 / ϵ , the QDMD algorithm provides an exponential acceleration of n , at the cost of greater dependence on M and ϵ . We test the effects of M on the QDMD algorithm in the specific application scenarios of data denoising, scene background extraction, and fluid dynamics analysis. We determined that the QDMD algorithm requires only a small number of samples M in specific applications, further demonstrating the quantum advantage of the QDMD algorithm in high-dimensional data analysis.
Accurate identification of Hamiltonian parameters is essential for modeling and controlling open quantum systems. In this work, we demonstrate that the multichannel Hankel alternative view of Koopman (mHAVOK) algorithm is a robust and reliable spectral data-driven method for retrieving Hamiltonian parameters from the evolution of first-moment observables in open quantum systems. The method relies on the discrete spectrum of the Koopman operator to obtain these parameters, which are computed using the mHAVOK algorithm; a theoretical connection to this affirmation is presented. The method is tested on noiseless quadratures of an open two-dimensional quantum harmonic oscillator and shown to retrieve oscillation frequencies, damping rates, nonlinear Kerr shifts, the qubit-photon coupling strength of a Jaynes-Cummings interaction, and the modulated frequency of a time-dependent Hamiltonian. The majority of the recovered parameters remained within 5% of their actual values. Compared with Fourier and matrix-pencil estimators, our approach yields lower errors for dynamics with strong dissipation. Overall, these findings suggest that Koopman operator theory provides a practical framework for studying quantum dynamical systems.