发表机构
North Carolina State University; University of Texas at Arlington（北卡罗来纳州立大学; 德克萨斯大学阿灵顿分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究分析了带Grover混合器的量子近似优化算法，证明了损失方差和导数的深度无关下界，并建立了Grover型可达性界，揭示了深度与初始概率的关系。
AI 中文摘要
我们研究了具有Grover混合器且代价和混合角度独立采样的量子近似优化算法。在初始态所携带的代价值满足一个格点条件的假设下，我们证明了在每一深度，损失方差的深度无关下界，以及关于最终混合角度导数的相同下界。该估计依赖于具体实例，并且对于固定局域性，对于具有一致有界局域项的整数值局域目标函数（特别是MaxCut），该下界与量子比特数成反多项式关系。我们还建立了Grover型可达性界，表明逼近一个指定的携带本征空间所需的深度被其初始概率的平方根倒数的常数倍所下界限制。
英文摘要
We study the Quantum Approximate Optimization Algorithm with a Grover mixer and independently sampled cost and mixing angles. Under a lattice condition on the cost values carried by the initial state, we prove a depth-independent lower bound for the variance of the loss at every depth, together with the same bound for the derivative with respect to the final mixing angle. The estimate is instance-dependent and, for fixed locality, is inverse polynomial in the number of qubits for integer-valued local objective functions with uniformly bounded local terms, in particular for MaxCut. We also establish Grover-type reachability bounds showing that the depth required to approximate a prescribed carried eigenspace is bounded below by a constant multiple of the inverse square root of its initial probability.
Comments23 pages, 4 figures
