标题： 量子近似优化算法的迭代插值调度 显示英文标题

标题： Iterative Interpolation Schedules for Quantum Approximate Optimization Algorithm

摘要： 量子近似优化算法（QAOA）是一种有前景的量子优化启发式方法，并且对于某些问题具有优于经典前沿算法的实证加速效果。 QAOA 使用一个带有 $p$ 层的参数化电路来解决优化问题，更高的 $p$ 会导致更好的解决方案。 现有方法需要优化 $2p$ 个独立参数，这对较大的 $p$ 来说是一项挑战。 在这项工作中，我们提出了一种迭代插值方法，通过使用正交函数基表示最优参数调度来利用其平滑性，推广了 Zhou 等人的工作。 通过优化少量基系数，并迭代增加电路深度和系数数量直到收敛，我们的方法能够为大型 $p$ 构建高质量的调度方案。 我们在三个问题上展示了我们的方法：Sherrington-Kirkpatrick (SK) 模型、投资组合优化以及低自相关二进制序列 (LABS)，其性能优于当前方法所需的更少的优化步骤。 对于最大的 LABS 实例，我们通过超过 1000 层的调度实现了接近最优的品质因数，这比以前的方法高出一个数量级。 作为我们技术的应用，我们观察到 QAOA 的深度增长较为温和即可精确解决 SK 模型，这是一个独立有趣的成果。 显示英文摘要

摘要： Quantum Approximate Optimization Algorithm (QAOA) is a promising quantum optimization heuristic with empirical evidence of speedup over classical state-of-the-art for some problems. QAOA solves optimization problems using a parameterized circuit with $p$ layers, with higher $p$ leading to better solutions. Existing methods require optimizing $2p$ independent parameters which is challenging for large $p$. In this work, we present an iterative interpolation method that exploits the smoothness of optimal parameter schedules by expressing them in a basis of orthogonal functions, generalizing Zhou et al. By optimizing a small number of basis coefficients and iteratively increasing both circuit depth and the number of coefficients until convergence, our approach enables construction of high-quality schedules for large $p$. We demonstrate our method achieves better performance with fewer optimization steps than current approaches on three problems: the Sherrington-Kirkpatrick (SK) model, portfolio optimization, and Low Autocorrelation Binary Sequences (LABS). For the largest LABS instance, we achieve near-optimal merit factors with schedules exceeding 1000 layers, an order of magnitude beyond previous methods. As an application of our technique, we observe a mild growth of QAOA depth sufficient to solve SK model exactly, a result of independent interest.