Certificates of quantum many-body properties assisted by machine learning

TL;DR

This paper introduces a novel method combining relaxation techniques with deep reinforcement learning to efficiently estimate bounds on quantum many-body ground state energies, outperforming classical algorithms and revealing phase transition indicators.

Contribution

The work presents a new hybrid approach that leverages relaxation and reinforcement learning to improve bounds in quantum optimization problems, with potential applications across quantum information processing.

Findings

The method effectively finds bounds on quantum ground state energies.

Transfer learning may indicate phase transitions.

The approach outperforms classical algorithms like Monte-Carlo.

Abstract

Computationally intractable tasks are often encountered in physics and optimization. Such tasks often comprise a cost function to be optimized over a so-called feasible set, which is specified by a set of constraints. This may yield, in general, to difficult and non-convex optimization tasks. A number of standard methods are used to tackle such problems: variational approaches focus on parameterizing a subclass of solutions within the feasible set; in contrast, relaxation techniques have been proposed to approximate it from outside, thus complementing the variational approach by providing ultimate bounds to the global optimal solution. In this work, we propose a novel approach combining the power of relaxation techniques with deep reinforcement learning in order to find the best possible bounds within a limited computational budget. We illustrate the viability of the method in the context of finding the ground state energy of many-body quantum systems, a paradigmatic problem in quantum physics. We benchmark our approach against other classical optimization algorithms such as breadth-first search or Monte-Carlo, and we characterize the effect of transfer learning. We find the latter may be indicative of phase transitions, with a completely autonomous approach. Finally, we provide tools to generalize the approach to other common applications in the field of quantum information processing.