Abstract
Efficient characterization of large-scale quantum systems, especially those produced by quantum analog simulators and megaquop quantum computers, poses a central challenge in quantum science owing to the exponential scaling of the Hilbert space with respect to system size. Recent advances in artificial intelligence (AI), with its aptitude for high-dimensional pattern recognition and function approximation, have emerged as a powerful tool to address this challenge. A growing body of research has leveraged AI to represent and characterize scalable quantum systems, spanning from theoretical foundations to experimental realizations. Depending on how previous knowledge and learning architectures are incorporated, the integration of AI into quantum system characterization can be categorized into three synergistic paradigms: machine learning, deep learning and language models. This Technical Review discusses how each of these AI paradigms contributes to two core tasks in representing and characterizing quantum systems: quantum property prediction and quantum system reconstruction. These tasks underlie a range of applications, from quantum certification and benchmarking to enhancing quantum algorithms and identifying critical quantum phenomena. We also discuss key challenges and open questions, together with future prospects at the interface of AI and quantum science.
Key points
Artificial intelligence models can be leveraged to represent and characterize scalable quantum systems in a data-driven manner, enabling quantum property prediction and approximate quantum system reconstruction
Provably efficient machine learning models have been designed to characterize linear properties of scalable quantum systems and to classify quantum phases
Deep learning models offer powerful tools for predicting a wide range of quantum properties through representation learning, as well as for implicitly reconstructing quantum systems using generative modelling approaches
Language models, building on the generative pre-trained transformer architecture, provide a flexible framework for auto-regressively representing large families of quantum states, paving the way towards foundation models for quantum systems and enabling new directions for research and application
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Subjects
- Computer science
- Quantum information
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Acknowledgements
Y.D. acknowledges the funding from A*STAR (H25-MRO3488) and NTU SUG (025257-00001). Y.-D.W. acknowledges funding from the National Natural Science Foundation of China through grant no. 12405022. J.E. acknowledges funding from the German BMFTR, Berlin Quantum, the Munich Quantum Valley, the Quantum Flagship (Millenion and PasQuans2), and the European Research Council. G.C. acknowledges support from the Hong Kong Research Grant Council through grant nos. SRFS2021-7S02, R7035-21F and 17310725. D.T. acknowledges the funding from NRF-P2024-001. Research at the Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Research, Innovation and Science.
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Authors and Affiliations
College of Computing and Data Science, Nanyang Technological University, Singapore, Singapore
Yuxuan Du & Dacheng Tao
School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore
Yuxuan Du
QICI Quantum Information and Computation Initiative, School of Computing and Data Science, The University of Hong Kong, Hong Kong, Hong Kong
Yan Zhu & Giulio Chiribella
Department of Physics, University of California, San Diego, La Jolla, CA, USA
Yuan-Hang Zhang & Yi-Zhuang You
Hon Hai (Foxconn) Research Institute, Taipei, Taiwan
Min-Hsiu Hsieh
Centre for Quantum Technologies, National University of Singapore, Singapore, Singapore
Patrick Rebentrost & Weibo Gao
Department of Computer Science, National University of Singapore, Singapore, Singapore
Patrick Rebentrost
School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore, Singapore
Weibo Gao
Dahlem Center for Complex Quantum Systems, Freie Universitat Berlin, Berlin, Germany
Jens Eisert
Helmholtz-Zentrum Berlin für Materialien und Energie, Berlin, Germany
Jens Eisert
Department of Computer Science, University of Oxford, Oxford, UK
Giulio Chiribella
Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada
Giulio Chiribella
Institute for Quantum Science and Technology, University of Calgary, Calgary, Alberta, Canada
Barry C. Sanders
John Hopcroft Center for Computer Science, Shanghai Jiao Tong University, Shanghai, China
Ya-Dong Wu
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Contributions
Y.D. and Y.-D.W. initiated the writing of this Technical Review and completed its first draft. M.-H.H., P.R. and W.G. contributed to the editing of the ‘Machine learning paradigm’ section, Y.Z. and Y.-Z.Y. contributed to the ‘Deep learning paradigm’ section, and Y.-H.Z. contributed to the ‘Language model paradigm’ section. J.E., G.C., D.T. and B.C.S. contributed to the overall editing of this Technical Review
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Glossary
Attention mechanisms
Neural-network operations that assign different weights to different parts of the input when constructing a representation, allowing the model to focus on the most relevant information for a given task; they are a key ingredient of transformer architectures and enables the efficient modelling of long-range dependencies and contextual relationships in complex data
Clifford circuits
Quantum circuits composed entirely of Clifford gates, that is, gates whose conjugation maps Pauli operators to Pauli operators; such circuits can be efficiently simulated classically using the Gottesman–Knill theorem
Convolutional neural network
(CNN). A deep learning architecture that uses convolutional layers to learn spatial and hierarchical features from grid-structured data, such as images
Fully connected neural network
(FCNN). A type of artificial neural network wherein each neuron in one layer is connected to every neuron in the adjacent layer
Graph neural networks
(GNNs). A class of neural networks designed to operate directly on graph-structured data by iteratively aggregating information from the neighbours of a node to learn representations that capture both node features and topological structure
Kernel machine
A class of machine learning models that performs prediction through a kernel function, which quantifies the similarity between data points in a feature space; by replacing explicit feature construction with kernel evaluation, it enables nonlinear learning while retaining a simple linear structure in the induced space; common examples include the Gaussian kernel, polynomial kernel and Dirichlet kernel, each suited to different structural properties of the target function
Kraus operators
Operators that provide a general mathematical framework for describing quantum channels, by representing any completely positive trace-preserving map as a sum of operators acting on a density matrix in the form ({sum }_{i}{K}_{i}rho {K}_{i}^{dagger }) with ({sum }_{i}{K}_{i}^{dagger }{K}_{i}={mathbb{I}})
Language models
A class of generative models, typically based on transformer architectures, that learn the statistical structure of sequences by modelling token probabilities conditioned on context; although originally developed for natural language, language models can also be applied to quantum systems
Long short-term memory
(LSTM). A specialized type of RNN that addresses the vanishing gradient problem through a gated cell structure, enabling it to learn long-range dependencies and remember information over extended sequences
Megaquop quantum computer
An error-corrected quantum computer capable of executing on the order of 1 million coherent quantum operations
Non-Clifford gates
Quantum gates that cannot be generated by Clifford circuits alone and are necessary for achieving universal quantum computing; examples are T gate and Toffoli gate
Positive operator-valued measure
(POVM). A set of positive semidefinite operators that sum to the identity, providing the most general mathematical description of a quantum measurement
Recurrent neural networks
(RNNs). A class of neural networks with recurrent connections and hidden states, designed to process sequential or time-dependent data
Su–Schrieffer–Heeger system
A 1D tight-binding model of a chain with alternating hopping amplitudes, which serves as a prototypical example of a topological insulator
Transformers
Neural-network architectures built on self-attention mechanisms, designed to model long-range dependencies in sequential or structured data; they serve as a foundation for modern large language models and have become a powerful tool for representation learning and generative modelling
Transverse-field Ising model
A model that describes a spin system with Ising interactions along one spin direction and an external field applied along a transverse direction; it is a paradigmatic model for studying quantum phase transitions, criticality and non-equilibrium quantum dynamics
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Du, Y., Zhu, Y., Zhang, YH. et al. Artificial intelligence for representing and characterizing quantum systems.
Nat Rev Phys (2026). https://doi.org/10.1038/s42254-026-00962-5
Accepted:01 June 2026
Published:29 July 2026
Version of record:29 July 2026
DOI
:https://doi.org/10.1038/s42254-026-00962-5
