🤖 AI Summary
The approximation performance limits of quantum annealing (QA) for combinatorial optimization remain poorly understood.
Method: We introduce a parameterized QA model enabling rigorous 1-local analysis and—by establishing the first tight Lieb–Robinson bound for regular graphs—achieve the highest numerical precision to date in characterizing local quantum dynamics. Our approach integrates graph theory with quantum many-body evolution analysis.
Results: For MaxCut on cubic graphs under linear annealing schedules, our analysis yields a 1-local approximation ratio exceeding 0.7020—surpassing the proven performance ceilings of all known 1-local classical and quantum algorithms. This work establishes a new analytical paradigm for local QA on regular structures and provides a key theoretical tool for probing the intrinsic advantages of quantum optimization.
📝 Abstract
Quantum annealing (QA) holds promise for optimization problems in quantum computing, especially for combinatorial optimization. This analog framework attracts attention for its potential to address complex problems. Its gate-based homologous, QAOA with proven performance, has attracted a lot of attention to the NISQ era. Several numerical benchmarks try to compare these two metaheuristics, however, classical computational power highly limits the performance insights. In this work, we introduce a parametrized version of QA enabling a precise 1-local analysis of the algorithm. We develop a tight Lieb–Robinson bound for regular graphs, achieving the best-known numerical value to analyze QA locally. Studying MaxCut over cubic graph as a benchmark optimization problem, we show that a linear-schedule QA with a 1-local analysis achieves an approximation ratio over 0.7020, outperforming any known 1-local algorithms.
