Deep Unfolded Local Quantum Annealing

TL;DR

This paper introduces a deep unfolded version of local quantum annealing that uses back-propagation to optimize parameters, significantly improving convergence speed and performance on complex models like the Sherrington-Kirkpatrick model.

Contribution

The paper presents a novel integration of deep unfolding with local quantum annealing, enabling parameter tuning through training data for better optimization performance.

Findings

Deep unfolded LQA outperforms original LQA in convergence speed.

Trained parameters generalize across instances and system sizes.

Significant practical implications for real-world optimization problems.

Abstract

Local quantum annealing (LQA), an iterative algorithm, is designed to solve combinatorial optimization problems. It draws inspiration from QA, which utilizes adiabatic time evolution to determine the global minimum of a given objective function. In the original LQA, the classical Hamiltonian is minimized via gradient descent. The performance of LQA depends on the choice of the parameters. Owing to the non-convex nature of the original cost function, LQA often becomes trapped in local minima, limiting its effectiveness. To address this challenge, we combine LQA with a deep unfolding scheme, which enables us to tune the parameters from the training data via back-propagation. {As a demonstration, we apply the deep unfolded LQA to the Sherrington-Kirkpatrick model, which is a fundamental {model} in statistical physics.} Our findings exhibit that deep unfolded LQA outperforms the original LQA, exhibiting remarkable convergence speed and performance improvement. As the trained parameters can be generalized to unknown instances and different system sizes, our results have significant practical implications and provide valuable insights for real-world applications.