Predicting properties of quantum systems by regression on a quantum computer

TL;DR

This paper introduces a quantum machine learning method using parametrized quantum circuits to predict continuous properties of quantum states, demonstrating high accuracy and potential to reach theoretical limits.

Contribution

The work presents a novel approach for quantum property regression using parametrized circuits, outperforming Bayesian methods in variance minimization.

Findings

Accurately predicts quantum state properties like entanglement and Hamiltonian parameters.

Can saturate the Cramer-Rao bound, indicating near-optimal prediction accuracy.

Outperforms Bayesian approach in variance minimization.

Abstract

Quantum computers can be considered as a natural means for performing machine learning tasks for inherently quantum labeled data. Many quantum machine learning techniques have been developed for solving classification problems, such as distinguishing between phases of matter or quantum processes. Similarly, one can consider a more general problem of regression, when the aim is to predict continuous labels quantifying properties of quantum states, such as purity or entanglement. In this work, we propose a method for predicting such properties. The method is based on the notion of parametrized quantum circuits, and it seeks to find an observable the expectation of which gives the prediction of the property of interest with a low variance. We numerically test our approach in learning to predict (i) the parameter of a parametrized channel given its output state, (ii) entanglement of two-qubit states, and (iii) the parameter of a parametrized Hamiltonian given its ground state. The results show that the proposed method is able to find observables such that they provide highly accurate predictions of the considered properties, and in some cases even saturate the Cramer-Rao bound, which characterizes the prediction error. We also compare our method with the Bayesian approach, and find that the latter prefers to minimize the prediction variance, having therefore a larger bias.