Learning to Classify Quantum Phases of Matter with a Few Measurements

TL;DR

This paper presents a supervised learning framework that leverages partial prior knowledge and combines classical and quantum techniques to classify quantum phases of matter efficiently with limited measurements.

Contribution

It introduces a novel method to classify quantum phases using a mix of classical and quantum tools, enabling phase identification with few measurements in unknown regions.

Findings

Polynomial measurement complexity for certifying new ground states

Effective classification of quantum phases in cold atom experiments

Integration of tensor networks, kernel methods, and quantum algorithms

Abstract

We study the identification of quantum phases of matter, at zero temperature, when only part of the phase diagram is known in advance. Following a supervised learning approach, we show how to use our previous knowledge to construct an observable capable of classifying the phase even in the unknown region. By using a combination of classical and quantum techniques, such as tensor networks, kernel methods, generalization bounds, quantum algorithms, and shadow estimators, we show that, in some cases, the certification of new ground states can be obtained with a polynomial number of measurements. An important application of our findings is the classification of the phases of matter obtained in quantum simulators, e.g., cold atom experiments, capable of efficiently preparing ground states of complex many-particle systems and applying simple measurements, e.g., single qubit measurements, but unable to perform a universal set of gates.