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 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 timereversal 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.

Machine learning on quantum experimental data toward solving quantum many-body problems

“…To generate data for ML, we prepared the fixed-point state of a given phase on the quantum computer and applied a local random unitary to generate different states within the same phase as the training data 36 . The advantage of this approach is that it allows for modelindependent data acquisition, thereby reducing the biases in the training data 37 . With a classical shadow that contains sufficient information to compute the nonlinear properties of the state, we employed a shadow kernel 18 defined by…”

“…As a fixed-point state in the SPT and trivial phases, we utilized the ground state of HZXZ = −∑iZi-1XiZi+1 and HX = −∑iXi with a 44-site periodic boundary condition, respectively, and examined whether the ML model can distinguish the SPT phase protected by ℤ2⊗ℤ2 symmetry generated by Xeven(odd) = ∏i=even(odd)Xi or time-reversal symmetry (TRS) 𝒯 = (∏iXi)K, where ℤ2 is a second-order group and K denotes complex conjugation. Specifically, we do not assume that the system is translationally invariant when applying a symmetric random unitary 37 (Fig. 3b).…”