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Communications Physics

Learning and forecasting open quantum dynamics with correlated noise

Xinfang Zhang, Zhihao Wu, Gregory A. L. White, Zhongcheng Xiang, Shun Hu, Zhihui Peng, Yong Liu, Dongning Zheng, Xiang Fu, Anqi Huang, Dario Poletti, Kavan Kishore Modi, Junjie Wu, Mingtang Deng, Chu Guo

Published Jan 18, 2025• 8 citations
Publisher

Abstract

The development of practical quantum processors relies on the ability to control and predict their functioning despite the presence of noise. This is particularly challenging for temporarily correlated noise. Here we propose a physics-inspired supervised machine learning approach to efficiently and accurately predict the functioning of quantum processors in the presence of correlated noise, which only requires data from randomized benchmarking experiments. To demonstrate the efficacy of our technique, we analyze the data from a superconducting quantum processor with tunable correlated noise. We produce training data by evolving the system for a number of time steps, and with this, we fully quantify the correlated noise and accurately predict the dynamics of the system for times beyond the training data. This approach shows a path towards efficient and effective learning of noisy quantum dynamics and optimally control quantum processors over long and complex computations even in the presence of correlated noise. Combining standard quantum benchmarking techniques with a physics-inspired supervised machine learning algorithm, the authors efficiently and accurately predict the functioning of a superconducting qubit in the presence of complex noise. The proposed approach opens a path towards a better control of current quantum devices.

DOI
10.1038/s42005-025-01944-2

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The development of practical quantum processors relies on the ability to control and predict their functioning despite the presence of noise. This is particularly challenging for temporarily correlated noise. Here we propose a physics-inspired supervised machine learning approach to efficiently and accurately predict the functioning of quantum processors in the presence of correlated noise, which only requires data from randomized benchmarking experiments. To demonstrate the efficacy of our technique, we analyze the data from a superconducting quantum processor with tunable correlated noise. We produce training data by evolving the system for a number of time steps, and with this, we fully quantify the correlated noise and accurately predict the dynamics of the system for times beyond the training data. This approach shows a path towards efficient and effective learning of noisy quantum dynamics and optimally control quantum processors over long and complex computations even in the presence of correlated noise. Combining standard quantum benchmarking techniques with a physics-inspired supervised machine learning algorithm, the authors efficiently and accurately predict the functioning of a superconducting qubit in the presence of complex noise. The proposed approach opens a path towards a better control of current quantum devices.
The development of fault-tolerant quantum processors relies on the ability to control noise. A particularly insidious form of noise is temporally correlated or non-Markovian noise. By combining randomized benchmarking with supervised machine learning algorithms, we develop a method to learn the details of temporally correlated noise. In particular, we can learn the time-independent evolution operator of system plus bath and this leads to (i) the ability to characterize the degree of non-Markovianity of the dynamics and (ii) the ability to predict the dynamics of the system even beyond the times we have used to train our model. We exemplify this by implementing our method on a superconducting quantum processor. Our experimental results show a drastic change between the Markovian and non-Markovian regimes for the learning accuracies.
Implementing fast and high-fidelity quantum operations using open-loop quantum optimal control relies on having an accurate model of the quantum dynamics. Any deviations between this model and the complete dynamics of the device, such as the presence of spurious modes or pulse distortions, can degrade the performance of optimal controls in practice. Here, we propose an experimentally simple approach to realize optimal quantum controls tailored to the device parameters and environment while specifically characterizing this quantum system. Concretely, we use physics-inspired machine learning to infer an accurate model of the dynamics from experimentally available data and then optimize our experimental controls on this trained model. We show the power and feasibility of this approach by optimizing arbitrary single-qubit operations on a superconducting transmon qubit, using detailed numerical simulations. We demonstrate that this framework produces an accurate description of the device dynamics under arbitrary controls, together with the precise pulses achieving arbitrary single-qubit gates with a high fidelity of about 99.99%.
Noisy quantum processors require precise and coherent quantum control to effectively execute quantum algorithms. Key to achieving precise control is the characterization of a quantum device to elucidate important details of environmentally-induced and systematic error sources. Quantum noise spectroscopy (QNS) is one such protocol used to characterize spatiotemporally correlated noise. QNS strives to provide estimates of noise statistical properties by using the quantum system as a dynamical probe. Despite its success, QNS can be challenging as it requires model selection prior to protocol implementation and suffers from scalability issues as system size grows. Here, we leverage machine learning to overcome model selection and assist in learning complex noise environments. In particular, we utilize physics-informed neural networks based on the “gray box” model to learn the dynamics of a two-qubit system subject to spatiotemporally correlated noise. Using training data sets based on dynamical decoupling, we show that the model is capable of learning the underlying power spectral densities for each qubit and the strength of parasitic qubit-qubit interactions. Furthermore, we show that the model can predict state-dependent behavior for multi-qubit observables. The results of this study further display the potential utility of machine learning to assist in the domain of quantum characterization and control.
Maximizing the computational utility of near-term quantum processors requires predictive noise models that inform robust, noise-aware compilation and error mitigation. Conventional models often fail to capture the complex error dynamics of real hardware or require prohibitive characterization overhead. We introduce a data-efficient framework that first constructs a physically motivated, parameterized noise model, and subsequently employs machine-learning-driven Bayesian optimization to identify its parameters. Our approach circumvents costly characterization protocols by estimating algorithm- and hardware-specific error parameters directly from readily available experimental data derived from existing application and benchmark circuit executions. The generality and robustness of the framework are demonstrated across diverse algorithms and superconducting devices, yielding high-fidelity predictions by estimating an independent parameter set tailored to each specific algorithm-hardware context. Crucially, we show that a model calibrated exclusively on small-scale circuits accurately predicts the behavior of larger validation circuits. Our data-efficient approach achieves up to a 65% improvement in model fidelity quantified by the Hellinger distance between predicted and experimental circuit output distributions, compared to standard noise models derived from device properties. This work establishes a practical paradigm for application-aware noise characterization, enabling compilation and error-mitigation strategies tailored to the specific interplay between quantum algorithms and device-specific noise dynamics.
Protecting quantum coherence against realistic environmental noise remains one of the fundamental obstacles to scalable quantum technologies. We develop a noise-adaptive dynamical decoupling framework that combines analytical open-quantum-system modeling with machine-learning-based forecasting for a qubit interacting with random telegraph noise. Unlike conventional dynamical decoupling protocols based on fixed pulse schedules, the proposed approach continuously forecasts short-time coherence evolution and adaptively applies control pulses according to the instantaneous noise dynamics. We investigate stationary and non-stationary environments spanning both Markovian and non-Markovian regimes. Numerical simulations demonstrate that the machine-learning-assisted adaptive control strategy substantially outperforms conventional periodic dynamical decoupling while using a comparable number of control pulses. The improvement becomes particularly pronounced in non-Markovian and non-stationary regimes, where memory effects, coherence revivals, and temporally evolving noise strongly limit the effectiveness of static pulse protocols. These results establish predictive machine-learning-assisted dynamical decoupling as a promising and scalable framework for adaptive quantum control in realistic noisy quantum devices.
In this paper, machine learning and artificial neural network models are proposed for quantum noise classification in stochastic quantum dynamics. For this purpose, we train and then validate support vector machine, multi-layer perceptron and recurrent neural network, models with different complexity and accuracy, to solve supervised binary classification problems. By exploiting the quantum random walk formalism, we demonstrate the high efficacy of such tools in classifying noisy quantum dynamics using data sets collected in a single realisation of the quantum system evolution. In addition, we also show that for a successful classification one just needs to measure, in a sequence of discrete time instants, the probabilities that the analysed quantum system is in one of the allowed positions or energy configurations, without any external driving. Thus, neither measurements of quantum coherences nor sequences of control pulses are required. Since in principle the training of the machine learning models can be performed a-priori on synthetic data, our approach is expected to find direct application in a vast number of experimental schemes and also for the noise benchmarking of the already available noisy intermediate-scale quantum devices.