Quantum kernels to learn the phases of quantum matter

TL;DR

This paper demonstrates how quantum kernel methods can effectively predict and classify quantum phases and phase transitions, providing interpretable results linked to quantum information concepts.

Contribution

It introduces quantum kernels for phase classification, linking learning with quantum fidelity, and develops algorithms for quantum processors to identify phases of matter.

Findings

Accurate phase transition predictions in the Ising model.

Successful extraction of critical exponents for larger systems.

Algorithms for phase classification on quantum hardware.

Abstract

Classical machine learning has succeeded in the prediction of both classical and quantum phases of matter. Notably, kernel methods stand out for their ability to provide interpretable results, relating the learning process with the physical order parameter explicitly. Here, we exploit quantum kernels instead. They are naturally related to the \emph{fidelity} and thus it is possible to interpret the learning process with the help of quantum information tools. In particular, we use a support vector machine (with a quantum kernel) to predict and characterize second order quantum phase transitions. We explain and understand the process of learning when the fidelity per site (rather than the fidelity) is used. The general theory is tested in the Ising chain in transverse field. We show that for small-sized systems, the algorithm gives accurate results, even when trained away from criticality. Besides, for larger sizes we confirm the success of the technique by extracting the correct critical exponent $\nu$. Finally, we present two algorithms, one based on fidelity and one based on the fidelity per site, to classify the phases of matter in a quantum processor.