Advantages of fixing spins in quantum annealing

TL;DR

This paper investigates the impact of fixing spins in quantum annealing, showing that choosing the right number of fixed spins improves solution quality and energy gap expansion in hybrid quantum-classical methods.

Contribution

It introduces a parameterized fixing spins method and demonstrates the importance of selecting the optimal number of fixed spins for better quantum annealing performance.

Findings

Proper fixing of spins enhances solution quality.

Fixing spins leads to energy gap expansion.

Optimal number of fixed spins is crucial for performance.

Abstract

Quantum annealing can efficiently obtain solutions to combinatorial optimization problems. Size-reduction methods are used to treat large-scale combinatorial optimization problems that cannot be input directly into a quantum annealer because of its size limitation. Various size-reduction methods using fixing spins have been proposed as quantum-classical hybrid methods to obtain solutions. However, the high performance of these hybrid methods is yet to be clearly elucidated. In this study, we adopted a parameterized fixing spins method to verify the effects of fixing spins. The results revealed that setting the appropriate number of spins of the subproblem is crucial for obtaining a satisfactory solution, and the energy gap expansion is confirmed after fixing spins.