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

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 wavefunctions of the quantum phase and then 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 towards hardware-efficient training of quantum phase classifiers on a programmable quantum processor.

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• Efficient MPS representations and quantum circuits from the Fourier modes of classical image data
• The role of data embedding in equivariant quantum convolutional neural networks
• Clifford Group and Unitary Designs under Symmetry
• Splitting and Parallelizing of Quantum Convolutional Neural Networks for Learning Translationally Symmetric Data
• Designs from Local Random Quantum Circuits with SU(d) Symmetry
• Simulating 2D topological quantum phase transitions on a digital quantum computer
• Error-tolerant quantum convolutional neural networks for symmetry-protected topological phases
• Noise-Robust Detection of Quantum Phase Transitions
• Uncovering Quantum Many-body Scars with Quantum Machine Learning
• Permutation-equivariant quantum convolutional neural networks
• Characterizing out-of-distribution generalization of neural networks: application to the disordered Su-Schrieffer-Heeger model
• Channel Attention for Quantum Convolutional Neural Networks
• Quantum Adjoint Convolutional Layers for Effective Data Representation
• Quantum Convolutional Neural Network for Phase Recognition in Two Dimensions
• Simulating Topological Order on Quantum Processors
• Quantum Phase Recognition via Quantum Attention Mechanism
• Quantum phase classification via partial tomography-based quantum hypothesis testing
• Learning complexity gradually in quantum machine learning models