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

TL;DR

This paper introduces a model-independent method for training quantum convolutional neural networks to identify quantum phases of matter and their order parameters, even under perturbations, facilitating efficient quantum phase classification.

Contribution

The authors propose a novel, model-independent training protocol for QCNNs that discovers robust order parameters and accurately classifies different quantum phases, including topological ones.

Findings

Successfully trained QCNN to identify phases protected by time-reversal symmetry.

Discovered order parameters that distinguish trivial, symmetry-breaking, and topological phases.

Accurately predicted phase boundaries in various models.

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.