发表机构
International Center for Quantum Optics and Quantum Technologies; National University of Science and Technology “MISIS”; Steklov Mathematical Institute of Russian Academy of Sciences（国际量子光学与量子技术研究中心; 莫斯科国立科技大学（MISIS）; 俄罗斯科学院斯捷克洛夫数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过弱纠缠QAOA机制提出BOND-1经典求解器，在无纠缠下仍保持高优化性能，表明纠缠在该机制中非必需。
AI 中文摘要
纠缠在量子优化中的作用仍是一个活跃的争论话题。为解答这一问题，我们聚焦于量子近似优化算法（QAOA）的固定参数扩展深度机制，其中紧凑的双参数调度在小规模实例上训练一次，随后随问题规模和电路深度的增加而应用。为超越全态矢量模拟来探测这一机制，我们进行了多达50个量子比特和100层的近似矩阵乘积态模拟，并通过键维数量化纠缠。我们观察到一种纠缠-解纠缠轮廓，其峰值键维数随深度增加而减小并最终饱和。这一观察激发了一种极端近似：在每次双量子比特相互作用后将态投影到乘积态流形（键维数为1）上。基于这一近似，我们引入了BOND-1，一种受量子启发的经典求解器。尽管进行了大幅简化，BOND-1在标准GSet MaxCut基准（变量数多达20000）上相对于已知最优值的割比超过0.95，在某些情况下甚至与之持平。它无需逐实例优化即可实现这些结果，且具有线性内存成本，而逐实例调优可提供进一步改进。这些结果表明，在该机制下，即使在完全无纠缠的情况下，QAOA的大部分优化能力仍然保留。然而，我们的结论仅限于此特定设置，并不暗示纠缠在一般量子优化中是不必要的。
英文摘要
The role of entanglement in quantum optimization remains actively debated. To address this question, we focus on the fixed-parameter expanding-depth regime of the quantum approximate optimization algorithm (QAOA), where a compact two-parameter schedule is trained once on small instances and then applied as the problem size and circuit depth increase. To probe this regime beyond full state-vector simulation, we perform approximate matrix product state simulations for up to 50 qubits and 100 layers and quantify entanglement by the bond dimension. We observe an entangle--disentangle profile, with the peak bond dimension decreasing with depth and eventually saturating. This observation motivates an extreme approximation: projecting the state onto the product-state manifold (bond dimension one) after every two-qubit interaction. Based on this approximation, we introduce BOND-1, a quantum-inspired classical solver. Despite the drastic simplification, BOND-1 achieves cut ratios above 0.95 relative to the best known values on standard GSet MaxCut benchmarks with up to 20000 variables, and in some cases it matches those values. It achieves these results without per-instance optimization and has linear memory cost, while per-instance tuning can provide further improvement. These results show that, in this regime, a substantial fraction of the optimization power of QAOA survives even in the complete absence of entanglement. Our conclusions, however, are specific to this setting and do not imply that entanglement is unnecessary for quantum optimization in general.
