基于浅度量子近似优化算法的热启动MaxCut松弛方法
Warm-Starting MaxCut Relaxation via Low-Depth Quantum Approximate Optimization Algorithm
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中文总结 AI 辅助
该研究提出基于QAOA局部关联子的热启动方法，初始化BM秩二松弛，在两类图优化问题上可快速得到优质解，虽迭代充足时随机基线略优，但浅度量子电路为经典优化提供了有用结构信息，为近期量子实用化开辟了路径。
中文摘要 AI 辅助
随着量子硬件性能不断提升，量子优化领域的研究兴趣日益浓厚，但最先进的经典求解器在实际应用中仍是极具竞争力的基准。本文未寻求完全替代经典优化的量子方案，而是提出一种混合策略，利用量子信息增强主流经典启发式算法。具体而言，我们引入一种基于量子近似优化算法（QAOA）得到的局部关联子的热启动（WS）方法，并用该信息初始化Burer-Monteiro（BM）秩二松弛。我们通过数值实验验证，与随机多启动初始化基线（BM的标准策略）相比，这种量子信息初始化在两类问题上能提供显著的初始优势：在n=500和n=1000量子比特的情况下，分别针对边密度为10%的随机Erdős Rényi图（ER-10）和全连接Sherrington Kirkpatrick（SK）自旋玻璃模型，该方法仅需极少迭代即可获得高质量解。同时，当迭代次数足够多时，随机基线通常最终能追上，且平均而言略优于热启动策略，这种效应在n=500时比n=1000时更为明显。结果表明，使用热启动可快速得到优质解，而通过标准策略投入更多迭代预算则能探索到更优解，二者存在探索与利用的权衡。本研究证明浅度量子电路可为经典优化提供有用的结构信息，为通过量子辅助初始化实现近期量子实用化提供了有前景的路径。
英文摘要
Quantum optimization has attracted growing interest as quantum hardware continues to improve, yet state-of-the-art classical solvers remain a formidable benchmark for practical utility. Rather than seeking a fully quantum replacement for classical optimization, we propose a hybrid strategy that uses quantum information to enhance leading classical heuristics. Specifically, we introduce a warm-start method based on local correlators obtained from the Quantum Approximate Optimization Algorithm (QAOA), and use this information to initialize the Burer-Monteiro (BM) rank-two relaxation. We demonstrate numerically that, compared to a random, multi-start initialization baseline (a standard strategy used for BM), this quantum-informed initialization offers a significant head start, i.e., high-quality solutions with very small number of iterations, for two problem classes -- random Erdős Rényi graphs with edge density of $10\%$ (ER-10) and fully-connected Sherrington Kirkpatrick (SK) spin glass models, at $n=500$ and $n=1000$ qubits. At the same time, given enough iterations, the random baseline often eventually catches up and slightly outperforms the warm-start strategy on average, an effect visibly stronger for $n=500$ than for $n=1000$. The results demonstrate an exploitation/exploration tradeoff of using WS to quickly arrive at very good solutions vs exploring slightly better solutions with a larger iterations budget via a standard strategy. Our results highlight how low-depth quantum circuits can provide useful structural information for classical optimization and suggest a promising route toward near-term quantum utility through quantum-assisted initialization.
