Machine learning phase transitions with a quantum processor
Open accessAbstract
Machine learning has emerged as a promising approach to unveil properties of many-body systems. Recently proposed as a tool to classify phases of matter, the approach relies on classical simulation methods---such as Monte Carlo---which are known to experience an exponential slowdown when simulating certain quantum systems. To overcome this slowdown while still leveraging machine learning, we propose a variational quantum algorithm which merges quantum simulation and quantum machine learning to classify phases of matter. Our classifier is directly fed labeled states recovered by the variational quantum eigensolver algorithm, thereby avoiding the data-reading slowdown experienced in many applications of quantum enhanced machine learning. We propose families of variational ansatz states that are inspired directly by tensor networks. This allows us to use tools from tensor network theory to explain properties of the phase diagrams the presented quantum algorithm recovers. Finally, we propose a majority vote quantum classifier built from a nearest-neighbor (checkerboard) quantum neural network. This classifier is successfully trained to recognize phases of matter with 99% accuracy for the transverse field Ising model and 94% accuracy for the $XXZ$ model. These findings suggest that a merger between quantum simulation and quantum enhanced machine learning offers a fertile ground to develop computational insights into quantum systems.
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Several quantum machine learning algorithms based on parameterized quantum circuits have demonstrated superior performance and computational abilities compared to conventional algorithms.
“Several QML algorithms based on PQC have been proposed [21–27], demonstrating superior performance and computational abilities compared to conventional algorithms [28–31].”
From Medical image diagnosis based on adaptive Hybrid Quantum CNN (2023) · cites this paper as [27]
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Miháliková, I., Krejčí, M., & Friák, M. (2025) · Scientific Reports · doi:10.1038/s41598-025-00151-x
Scaling Hybrid Quantum--HPC Applications with the Quantum Framework
Chundury, S., Shehata, A., Kim, S., Meena, M. G., Lu, C., Gottiparthi, K. C., Pérez, E. A. C., Mueller, F., & Suh, I. (2025) · International Conference for High Performance Computing, Networking, Storage and Analysis (SC) · doi:10.1145/3731599.3767553
Unsupervised learning to recognize quantum phases of matter
Khosrojerdi, M., Cuccoli, A., Verrucchi, P., & Banchi, L. (2026) · AVS Quantum Science · doi:10.1116/5.0332778
Li, D., Yang, X., Wang, X., & Zhang, W. (2026) · Advanced Intelligent Systems · doi:10.1002/aisy.202600009
A quantum-imaginary-time-evolution-based simulation of parallel mutation-selection-drift model
Jiang, L., Xiao, G., Dai, G., He, K., Cheng, M., Yang, L., Chang, J., Liu, J., & Chen, W. (2026) · Physics Letters A · doi:10.1016/j.physleta.2026.131896
- Authors
- Uvarov, A. V., Kardashin, A. S., & Biamonte, J. D.
- Affiliations
- Skolkovo Institute of Science and Technology (RU)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2020-07-15
- Volume
- 102
- Issue
- 1
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W2955078219
- Cited by
- 69
- References
- 38
- Citations by year
- 2026: 3 · 2025: 8 · 2024: 12 · 2023: 11 · 2022: 17 · 2021: 11 · 2020: 7
- FWCI
- 4.52
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Russian Foundation for Basic Research (19-31-90159)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- phase transitions, quantum machine learning, variational quantum eigensolver, variational ansatz, tensor networks, quantum neural networks, transverse-field Ising model, XXZ model, quantum simulation
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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