Quantitative analysis of the effectiveness of mid-anneal measurement in quantum annealing

TL;DR

This paper evaluates mid-anneal measurement in quantum annealing, showing it improves solution quality especially when energy states are close and scales well with system size, aiding optimization under noise.

Contribution

It introduces a quantitative metric for mid-anneal measurement effectiveness and analyzes its physical mechanisms and scalability in quantum annealing.

Findings

Most effective when energy differences are small

Effectiveness increases with smaller Hamming distance

Persists with increasing system size

Abstract

Quantum annealing is a promising metaheuristic for solving constrained combinatorial optimization problems. However, parameter tuning difficulties and hardware noise often prevent optimal solutions from being properly encoded as the ground states of the problem Hamiltonian. This study investigates mid-anneal measurement as a mitigation approach for such situations, analyzing its effectiveness and underlying physical mechanisms. We introduce a quantitative metric to evaluate the effectiveness of mid-anneal measurement and apply it to the graph bipartitioning problem and the quadratic knapsack problem. Our findings reveal that mid-anneal measurement is most effective when the energy difference between desired solutions and ground states is small, with effectiveness strongly governed by the energy structure. Furthermore, the effectiveness increases as the Hamming distance between the ground and excited states gets small, highlighting the role of state similarity. Analysis of fully-connected Ising models demonstrates that the effectiveness of mid-anneal measurement persists with increasing system size, indicating its scalability and practical applicability to large-scale quantum annealing.