Model-Independent Learning of Quantum Phases of Matter with Quantum Convolutional Neural Networks

Liu, Yu-Jie; Smith, Adam; Knap, Michael; Pollmann, Frank

Abstract

Quantum convolutional neural networks (QCNNs) have been introduced as classifiers for gapped quantum phases of matter. Here, we propose a model-independent protocol for training QCNNs to discover order parameters that are unchanged under phase-preserving perturbations. We initiate the training sequence with the fixed-point wave functions of the quantum phase and add translation-invariant noise that respects the symmetries of the system to mask the fixed-point structure on short length scales. We illustrate this approach by training the QCNN on phases protected by time-reversal symmetry in one dimension, and test it on several time-reversal symmetric models exhibiting trivial, symmetry-breaking, and symmetry-protected topological order. The QCNN discovers a set of order parameters that identifies all three phases and accurately predicts the location of the phase boundary. The proposed protocol paves the way toward hardware-efficient training of quantum phase classifiers on a programmable quantum processor.

Citation

Liu, Y., Smith, A., Knap, M., & Pollmann, F. (2023). Model-Independent Learning of Quantum Phases of Matter with Quantum Convolutional Neural Networks. Physical Review Letters, 130(22), Article 220603. https://doi.org/10.1103/physrevlett.130.220603

• Journal Article Type: Article
• Acceptance Date: May 16, 2023
• Online Publication Date: Jun 2, 2023
• Publication Date: Jun 2, 2023
• Deposit Date: Jun 22, 2023
• Publicly Available Date: Jul 4, 2023
• Journal: Physical Review Letters
• Print ISSN: 0031-9007
• Electronic ISSN: 1079-7114
• Publisher: American Physical Society (APS)
• Peer Reviewed: Peer Reviewed
• Volume: 130
• Issue: 22
• Article Number: 220603
• DOI: https://doi.org/10.1103/physrevlett.130.220603
• Public URL: https://nottingham-repository.worktribe.com/output/21646173
• Publisher URL: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.220603