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:2110.10721 · Physical Review A

Learning quantum dynamics with latent neural ordinary differential equations

Matthew Choi, Daniel Flam-Shepherd, Thi Ha Kyaw, Alán Aspuru‐Guzik

Published Apr 4, 2022• 26 citations
arXivHTMLPDF

Abstract

The core objective of machine-assisted scientific discovery is to learn physical laws from experimental data without prior knowledge of the systems in question. In the area of quantum physics, making progress towards these goals is significantly more challenging due to the curse of dimensionality as well as the counterintuitive nature of quantum mechanics. Here we present the QNODE, a latent neural ordinary differential equation (ODE) trained on expectation values of closed and open-quantum-systems dynamics. It can learn to generate such measurement data and extrapolate outside of its training region that satisfies the von Neumann and time-local Lindblad master equations for closed and open quantum systems, respectively, in an unsupervised means. Furthermore, the QNODE rediscovers quantum-mechanical laws such as the Heisenberg's uncertainty principle in a data-driven way, without any constraint or guidance. Additionally, we show that trajectories that are generated from the QNODE that are close in its latent space have similar quantum dynamics while preserving the physics of the training system.

DOI
10.1103/physreva.105.042403

Related papers

Quantum Filtering and Stabilization of Dissipative Quantum Systems via Augmented Neural Ordinary Differential Equations

Qamar, Shahid, Mushtaq Rana Imran, Bo Li +1 more

Modeling open quantum dynamics without full knowledge of the system Hamiltonian or noise model is a key challenge in quantum control and quantum state estimation. We introduce an Augmented Quantum Neural Ordinary Differential Equation (AQNODE) framework that learns quantum trajectories and dissipation parameters directly from partial continuous measurement data. By embedding the system into a latent space evolved via neural ODEs, AQNODE captures both observable and hidden non-Markovian dynamics with temporal smoothness and physical consistency. Our approach integrates weak measurement data to reconstruct qubit states and time-dependent decoherence rates, enabling accurate state prediction and parameter inference without explicit physical equations. Furthermore, we incorporate AQNODE-based feedback control techniques, including proportional-derivative and time-varying linear-quadratic regulator (LQR) strategies, to steer the quantum system toward target states in real time. Extensive numerical simulations demonstrate AQNODE's ability to generalize across system configurations, achieve low prediction errors, and perform robust quantum filtering and control. These results establish AQNODE as a scalable, differentiable, and experimentally compatible framework for real-time modeling and control of dissipative quantum systems.

arXiv:2509.07196•Sep 8, 2025•0 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

Learning quantum dissipation by the neural ordinary differential equation

Li Chen, Yadong Wu

Quantum dissipation arises from the unavoidable coupling between a quantum system and its surrounding environment, which is known as a major obstacle in the quantum processing of information. Apart from its existence, examining how to trace dissipation from observational data is important and may stimulate ways to suppress the dissipation. In this paper, we propose to learn about quantum dissipation from dynamical observations using the neural ordinary differential equation, and then demonstrate this method concretely on two open quantum-spin systems: A large spin system and a spin-1/2 chain. We also investigate the learning efficiency of the dataset, which provides useful guidance for data acquisition in experiments. Our work helps to facilitate effective modeling and decoherence suppression in open quantum systems.

arXiv:2207.09056•Physical Review A•Aug 1, 2022•5 citations

Lindbladian Learning with Neural Differential Equations

Timothy Heightman, Roman Aseguinolaza Gallo, Edward Jiang +3 more

Inferring the dynamical generator of a many-body quantum system from measurement data is essential for the verification, calibration, and control of quantum processors. When the system is open, this task becomes considerably harder than in the purely unitary case, because coherent and dissipative mechanisms can produce similar measurement statistics and long-time data can be insensitive to coherent couplings. Here we tackle this so-called Lindbladian learning problem of open-system characterisation with maximum-likelihood on Pauli measurements at multiple experimentally friendly \emph{transient} times, exploiting the richer information content of transient dynamics. To navigate the resulting non-convex likelihood loss-landscape, we augment the physical model neural differential-equation term, which is progressively removed during training to distil an interpretable Lindbladian solution. Our method reliably learns open-system dynamics across neutral-atom (with 2D connectivity) and superconducting Hamiltonians, as well as the Heisenberg XYZ, and PXP models on a spin-1/2 chain. For the dissipative part, we show robustness over phase noise, thermal noise, and their combination. Our algorithm can robustly infer these dissipative systems over noise-to-signal ratios spanning four orders of magnitude, and system sizes up to $N=6$ qubits with fewer than $5 \times 10^5$ shots.

quant-pharXiv:2603.07778•Mar 10, 2026•0 citations

Data-driven characterization of latent dynamics on quantum testbeds

Sohail R. Reddy, Stefanie Günther, Yujin Cho

This paper presents a data-driven approach to learn latent dynamics in superconducting quantum computing hardware. To this end, we augment the dynamical equation of quantum systems described by the Lindblad master equation with a parameterized source term that is trained from experimental data to capture unknown system dynamics, such as environmental interactions and system noise. We consider a structure preserving augmentation that learns and distinguishes unitary from dissipative latent dynamics parameterized by a basis of linear operators, as well as an augmentation given by a nonlinear feed-forward neural network. Numerical results are presented using data from two different quantum processing units (QPUs) at Lawrence Livermore National Laboratory's Quantum Device and Integration Testbed. We demonstrate that our interpretable, structure preserving, and nonlinear models are able to improve the prediction accuracy of the Lindblad master equation and accurately model the latent dynamics of the QPUs.

arXiv:2401.09822•AVS Quantum Science•Jul 18, 2024•0 citations

Accelerating Quantum Emitter Characterization with Latent Neural Ordinary Differential Equations

Andrew H. Proppe, Kin Long Kelvin Lee, Weiwei Sun +3 more

Deep neural network models can be used to learn complex dynamics from data and reconstruct sparse or noisy signals, thereby accelerating and augmenting experimental measurements. Evaluating the quantum optical properties of solid-state single-photon emitters is a time-consuming task that typically requires interferometric photon correlation experiments, such as Photon correlation Fourier spectroscopy (PCFS) which measures time-resolved single emitter lineshapes. Here, we demonstrate a latent neural ordinary differential equation model that can forecast a complete and noise-free PCFS experiment from a small subset of noisy correlation functions. By encoding measured photon correlations into an initial value problem, the NODE can be propagated to an arbitrary number of interferometer delay times. We demonstrate this with 10 noisy photon correlation functions that are used to extrapolate an entire de-noised interferograms of up to 200 stage positions, enabling up to a 20-fold speedup in experimental acquisition time from $\sim$3 hours to 10 minutes. Our work presents a new approach to greatly accelerate the experimental characterization of novel quantum emitter materials using deep learning.

arXiv:2411.11191•Nov 17, 2024•0 citations
The core objective of machine-assisted scientific discovery is to learn physical laws from experimental data without prior knowledge of the systems in question. In the area of quantum physics, making progress towards these goals is significantly more challenging due to the curse of dimensionality as well as the counterintuitive nature of quantum mechanics. Here we present the QNODE, a latent neural ordinary differential equation (ODE) trained on expectation values of closed and open-quantum-systems dynamics. It can learn to generate such measurement data and extrapolate outside of its training region that satisfies the von Neumann and time-local Lindblad master equations for closed and open quantum systems, respectively, in an unsupervised means. Furthermore, the QNODE rediscovers quantum-mechanical laws such as the Heisenberg's uncertainty principle in a data-driven way, without any constraint or guidance. Additionally, we show that trajectories that are generated from the QNODE that are close in its latent space have similar quantum dynamics while preserving the physics of the training system.
Modeling open quantum dynamics without full knowledge of the system Hamiltonian or noise model is a key challenge in quantum control and quantum state estimation. We introduce an Augmented Quantum Neural Ordinary Differential Equation (AQNODE) framework that learns quantum trajectories and dissipation parameters directly from partial continuous measurement data. By embedding the system into a latent space evolved via neural ODEs, AQNODE captures both observable and hidden non-Markovian dynamics with temporal smoothness and physical consistency. Our approach integrates weak measurement data to reconstruct qubit states and time-dependent decoherence rates, enabling accurate state prediction and parameter inference without explicit physical equations. Furthermore, we incorporate AQNODE-based feedback control techniques, including proportional-derivative and time-varying linear-quadratic regulator (LQR) strategies, to steer the quantum system toward target states in real time. Extensive numerical simulations demonstrate AQNODE's ability to generalize across system configurations, achieve low prediction errors, and perform robust quantum filtering and control. These results establish AQNODE as a scalable, differentiable, and experimentally compatible framework for real-time modeling and control of dissipative quantum systems.
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.
Quantum dissipation arises from the unavoidable coupling between a quantum system and its surrounding environment, which is known as a major obstacle in the quantum processing of information. Apart from its existence, examining how to trace dissipation from observational data is important and may stimulate ways to suppress the dissipation. In this paper, we propose to learn about quantum dissipation from dynamical observations using the neural ordinary differential equation, and then demonstrate this method concretely on two open quantum-spin systems: A large spin system and a spin-1/2 chain. We also investigate the learning efficiency of the dataset, which provides useful guidance for data acquisition in experiments. Our work helps to facilitate effective modeling and decoherence suppression in open quantum systems.
Inferring the dynamical generator of a many-body quantum system from measurement data is essential for the verification, calibration, and control of quantum processors. When the system is open, this task becomes considerably harder than in the purely unitary case, because coherent and dissipative mechanisms can produce similar measurement statistics and long-time data can be insensitive to coherent couplings. Here we tackle this so-called Lindbladian learning problem of open-system characterisation with maximum-likelihood on Pauli measurements at multiple experimentally friendly \emph{transient} times, exploiting the richer information content of transient dynamics. To navigate the resulting non-convex likelihood loss-landscape, we augment the physical model neural differential-equation term, which is progressively removed during training to distil an interpretable Lindbladian solution. Our method reliably learns open-system dynamics across neutral-atom (with 2D connectivity) and superconducting Hamiltonians, as well as the Heisenberg XYZ, and PXP models on a spin-1/2 chain. For the dissipative part, we show robustness over phase noise, thermal noise, and their combination. Our algorithm can robustly infer these dissipative systems over noise-to-signal ratios spanning four orders of magnitude, and system sizes up to N=6N=6N=6 qubits with fewer than 5×1055 \times 10^55×105 shots.
This paper presents a data-driven approach to learn latent dynamics in superconducting quantum computing hardware. To this end, we augment the dynamical equation of quantum systems described by the Lindblad master equation with a parameterized source term that is trained from experimental data to capture unknown system dynamics, such as environmental interactions and system noise. We consider a structure preserving augmentation that learns and distinguishes unitary from dissipative latent dynamics parameterized by a basis of linear operators, as well as an augmentation given by a nonlinear feed-forward neural network. Numerical results are presented using data from two different quantum processing units (QPUs) at Lawrence Livermore National Laboratory's Quantum Device and Integration Testbed. We demonstrate that our interpretable, structure preserving, and nonlinear models are able to improve the prediction accuracy of the Lindblad master equation and accurately model the latent dynamics of the QPUs.
Deep neural network models can be used to learn complex dynamics from data and reconstruct sparse or noisy signals, thereby accelerating and augmenting experimental measurements. Evaluating the quantum optical properties of solid-state single-photon emitters is a time-consuming task that typically requires interferometric photon correlation experiments, such as Photon correlation Fourier spectroscopy (PCFS) which measures time-resolved single emitter lineshapes. Here, we demonstrate a latent neural ordinary differential equation model that can forecast a complete and noise-free PCFS experiment from a small subset of noisy correlation functions. By encoding measured photon correlations into an initial value problem, the NODE can be propagated to an arbitrary number of interferometer delay times. We demonstrate this with 10 noisy photon correlation functions that are used to extrapolate an entire de-noised interferograms of up to 200 stage positions, enabling up to a 20-fold speedup in experimental acquisition time from $\sim$3 hours to 10 minutes. Our work presents a new approach to greatly accelerate the experimental characterization of novel quantum emitter materials using deep learning.