Frustration-Enhanced Quantum Annealing Correction Models with Additional Inter-replica Interactions

Abstract: Quantum annealing correction (QAC) models provide a promising approach for mitigating errors in quantum annealers. Previous studies have established that QAC models are crucial for ensuring the robustness of the ground state of the Ising model on hardware. In this work, the effects of QAC models incorporating replicas with additional interactions, specifically, the penalty spin model and the stacked model, are investigated for problems characterized by a small energy gap between the ground and first excited states during quantum annealing, a well-known bottleneck to reaching the ground state. The results demonstrate that these QAC models can obtain the optimal solution within short annealing times by exploiting diabatic transitions, even for problems with a small energy gap. These findings highlight the potential of QAC models as practical near-term algorithms for hardware subject to runtime limitations and control noise.