Efficient inference in the transverse field Ising model

TL;DR

This paper presents a novel approximate method for solving quantum cavity equations in transverse field Ising models, enabling efficient analysis of highly connected networks with improved accuracy and scalability.

Contribution

The paper introduces a projective approximation technique that explicitly separates classical and quantum parts of distributions, advancing inference methods for quantum many-body systems.

Findings

Accurate results compared to exact solutions and other methods

Linear computational complexity with network connectivity

Effective for highly connected quantum networks

Abstract

In this paper we introduce an approximate method to solve the quantum cavity equations for transverse field Ising models. The method relies on a projective approximation of the exact cavity distributions of imaginary time trajectories (paths). A key feature, novel in the context of similar algorithms, is the explicit separation of the classical and quantum parts of the distributions. Numerical simulations show accurate results in comparison with the sampled solution of the cavity equations, the exact diagonalization of the Hamiltonian (when possible) and other approximate inference methods in the literature. The computational complexity of this new algorithm scales linearly with the connectivity of the underlying lattice, enabling the study of highly connected networks, as the ones often encountered in quantum machine learning problems.