Solving Classical and Quantum Spin Glasses with Deep Boltzmann Quantum States

TL;DR

This paper introduces Deep Boltzmann Quantum States, a neural network approach inspired by deep Boltzmann machines, that efficiently tackles classical and quantum spin glasses and complex optimization problems.

Contribution

The authors develop a novel neural quantum state framework with efficient sampling and training algorithms, enabling solutions to large, complex disordered systems and optimization problems beyond current quantum hardware capabilities.

Findings

Successfully match exact or best estimates for classical and quantum spin glasses.

Solve NP-hard Job Shop Scheduling Problems exceeding quantum annealing hardware limits.

Demonstrate the effectiveness of the approach on large-scale disordered systems.

Abstract

Variational neural network models have achieved remarkable success in solving ground-state problems of quantum many-body systems. However, addressing classical and quantum spin glasses remains challenging, as disorder and energy frustration give rise to an exponentially large number of local energy minima separated by high-energy barriers, hindering the efficiency of conventional Metropolis-based Monte Carlo methods. To bridge this gap, we introduce Deep Boltzmann Quantum States, a class of neural quantum states inspired by deep Boltzmann machines that inherit efficient block Gibbs sampling. We also propose two key advances in the training algorithm. Firstly, we combine natural-gradient updates with state-of-the-art stochastic optimizers. Secondly, we gradually tune the hardness of the problem Hamiltonian by interpolating from an easy to a hard regime, without the need to closely approximate the instantaneous adiabatic state at intermediate times. We match the exact solution or the best available estimate for several instances of classical and quantum Ising spin-glass models with infinite-range interactions and hundreds of spins. We also solve instances of the NP-hard Job Shop Scheduling Problem exceeding the current limitations of quantum annealing hardware. To summarize, deep neural architectures with efficient global update rules and trained within an annealing-like scheme, provide a powerful framework for solving real-world hard combinatorial optimization and for investigating disordered quantum many-body systems.