只优化部分量子层，提升最大割问题求解效率
Investigating layer-selective transfer learning of QAOA parameters for Max-Cut problem
- 仅对转移参数后的部分量子层进行优化
- 在更低计算时间下保持良好解的质量
- 适合追求效率的量子优化应用场景
量子近似优化算法（QAOA）是一种适用于噪声中等规模量子（NISQ）处理器的变分量子算法，对组合优化问题（COP）表现优异。已有观察表明，一个实例的最优参数可迁移至另一实例，从而为后者提供较优解。本文提出一种改进方案：在参数迁移后，仅优化QAOA电路中部分层级。其动机在于降低高深度电路全层优化时的损失景观复杂度及优化耗时。针对最大割问题，我们探究了不同层级的潜在层次作用，并分析了近似比随问题规模增长的变化规律。结果表明，选择性层优化在解质量与计算时间间取得有利权衡，且在较低优化时间内优于全层优化。
原文摘要 · Abstract (English)
The quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm (VQA) ideal for noisy intermediate-scale quantum (NISQ) processors, and is highly successful in solving combinatorial optimization problems (COPs). It has been observed that the optimal parameters obtained from one instance of a COP can be transferred to another instance, resulting in generally good solutions for the latter. In this work, we propose a refinement scheme in which only a subset of QAOA layers is optimized following parameter transfer, with a focus on the Max-Cut problem. Our motivation is to reduce the complexity of the loss landscape when optimizing all the layers of high-depth QAOA circuits, as well as to reduce the optimization time. We investigate the potential hierarchical roles of different layers and analyze how the approximation ratio scales with increasing problem size. Our findings indicate that the selective layer optimization scheme offers a favorable trade-off between solution quality and computational time, and can be more beneficial than full optimization at a lower optimization time.
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