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arXiv:2207.09056 · Physical Review A

Learning quantum dissipation by the neural ordinary differential equation

Li Chen, Yadong Wu

Published Aug 1, 2022• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.106.022201

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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.
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.
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.
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.
Dissipation is usually viewed as an obstacle to predicting quantum dynamics, yet it can also contract trajectories toward steady states and thereby suppress accumulated prediction errors, leaving it unclear whether dissipation ultimately helps or hinders the learnability of open quantum dynamics. We investigate this question using Neural Ordinary Differential Equation (NODE) surrogates for open Heisenberg XYZ spin chains. Closed-system learnability deteriorates rapidly with system size, culminating in a static-prediction collapse at four qubits; dissipation reverses this trend, creating a broad high-fidelity regime at intermediate system sizes, while at four qubits a fidelity-aware objective recovers learnable rollout structure that is absent under closed-system training. Comparison against static and steady-state baselines reveals that dissipation improves performance through two fundamentally different mechanisms: at weak-to-moderate dissipation the surrogate captures nontrivial transient dynamics and substantially outperforms trivial predictors, whereas at stronger damping high fidelity increasingly reflects trajectory simplification toward the steady state rather than improved learned dynamics. These results show that dissipation can enhance the learnability of open quantum dynamics, but that fidelity alone is insufficient to distinguish genuine dynamical learning from steady-state trivialization: dissipative contraction and trajectory simplification are distinct effects that peak in different regimes and should be disentangled when evaluating learned quantum-dynamical surrogates.
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.
Simulating non-Markovian quantum dissipative dynamics remains a major challenge in theoretical and computational chemistry. While traditional numerical methods such as hierarchical equations of motion are numerically exact, they suffer from prohibitive computational costs when modeling systems with complex environmental couplings or strong non-Markovian effects. To address this limitation, we propose a deep learning framework based on two-dimensional convolutional neural networks (2D-CNN) for efficiently predicting long-time quantum dissipative dynamics using only short-time trajectory data. Our approach incorporates a 1D-to-2D feature reconstruction strategy, which transforms 1D time-series data into 2D images, and a multi-timescale fusion network to resolve complex dynamical features. We validate the framework on two paradigmatic cases — dissipative relaxation in a two-level system and Rabi oscillations in a dissipative spin system — achieving prediction mean absolute errors of 10−310^{-3}10−3 and 10−2,10^{-2},10−2, respectively. The results highlight the effectiveness of our 2D-CNN approach in capturing long-time temporal correlations, providing a computationally efficient pathway for simulating quantum dynamics in realistic open systems.