Learning of error statistics for the detection of quantum phases

TL;DR

This paper introduces a neural network-based classifier that detects quantum phase boundaries by analyzing error statistics on reference states, applicable to various gapped quantum phases.

Contribution

It presents a novel approach using neural networks trained on error data to identify phase boundaries in gapped quantum systems.

Findings

Successfully detects phase boundaries in different quantum phases.

Applies to systems with symmetry-breaking, symmetry-protected, and intrinsic topological order.

Demonstrates effectiveness with matrix product state calculations.

Abstract

We present a binary classifier based on neural networks to detect gapped quantum phases. By considering the errors on top of a suitable reference state describing the gapped phase, we show that a neural network trained on the errors can capture the correlation between the errors and can be used to detect the phase boundaries of the gapped quantum phase. We demonstrate the application of the method for matrix product state calculations for different quantum phases exhibiting local symmetry-breaking order, symmetry-protected topological order, and intrinsic topological order.