Quantum Gaussian process regression

TL;DR

This paper introduces a quantum algorithm for Gaussian process regression that significantly accelerates computation, utilizing novel sub-algorithms for mean and covariance prediction, and improved Hamiltonian simulation techniques.

Contribution

The paper presents a new quantum Gaussian process regression algorithm with three sub-algorithms, including an improved HHL method, achieving quadratic speedup over classical methods.

Findings

Achieves quadratic speedup over classical Gaussian process regression

Proposes an improved HHL algorithm for outcome sign determination

Uses Hamiltonian simulation and kernel techniques for covariance prediction

Abstract

In this paper, a quantum algorithm based on gaussian process regression model is proposed. The proposed quantum algorithm consists of three sub-algorithms. One is the first quantum subalgorithm to efficiently generate mean predictor. The improved HHL algorithm is proposed to obtain the sign of outcomes. Therefore, the terrible situation that results is ambiguous in terms of original HHL algorithm is avoided, which makes whole algorithm more clear and exact. The other is to product covariance predictor with same method. Thirdly, the squared exponential covariance matrices are prepared that annihilation operator and generation operator are simulated by the unitary linear decomposition Hamiltonian simulation and kernel function vectors is generated with blocking coding techniques on covariance matrices. In addition, it is shown that the proposed quantum gaussian process regression algorithm can achieve quadratic faster over the classical counterpart.