The quantum Gaussian process state: A kernel-inspired state with quantum support data

TL;DR

This paper introduces the quantum Gaussian process state, a new quantum state representation inspired by kernel methods, offering a compact, flexible, and efficiently trainable model that outperforms existing approaches in certain quantum physics applications.

Contribution

The paper presents the quantum Gaussian process state, a novel kernel-inspired quantum state with superior variational flexibility and efficient training capabilities for quantum many-body problems.

Findings

Competitive or superior variational flexibility compared to existing methods

Efficient deterministic training from small datasets

Enhanced generalization in frustrated spin physics applications

Abstract

We introduce the quantum Gaussian process state, motivated via a statistical inference for the wave function supported by a data set of unentangled product states. We show that this condenses down to a compact and expressive parametric form, with a variational flexibility shown to be competitive or surpassing established alternatives. The connections of the state to its roots as a Bayesian inference machine as well as matrix product states, also allow for efficient deterministic training of global states from small training data with enhanced generalization, including on application to frustrated spin physics.