Quantum annealing with symmetric subspaces

TL;DR

This paper introduces a symmetry-preserving drive Hamiltonian for quantum annealing, which confines the search to a symmetric subspace, thereby reducing non-adiabatic transitions and improving solution fidelity.

Contribution

The authors propose a novel drive Hamiltonian that maintains symmetry during quantum annealing, enhancing efficiency by suppressing unwanted non-adiabatic transitions.

Findings

Scheme outperforms conventional QA in fidelity

Uses XY model as drive Hamiltonian

Operates within symmetric subspace

Abstract

Quantum annealing (QA) is a promising approach for not only solving combinatorial optimization problems but also simulating quantum many-body systems such as those in condensed matter physics. However, non-adiabatic transitions constitute a key challenge in QA. The choice of the drive Hamiltonian is known to affect the performance of QA because of the possible suppression of non-adiabatic transitions. Here, we propose the use of a drive Hamiltonian that preserves the symmetry of the problem Hamiltonian for more efficient QA. Owing to our choice of the drive Hamiltonian, the solution is searched in an appropriate symmetric subspace during QA. As non-adiabatic transitions occur only inside the specific subspace, our approach can potentially suppress unwanted non-adiabatic transitions. To evaluate the performance of our scheme, we employ the XY model as the drive Hamiltonian in order to find the ground state of problem Hamiltonians that commute with the total magnetization along the $z$ axis. We find that our scheme outperforms the conventional scheme in terms of the fidelity between the target ground state and the states after QA.