发表机构
State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications; State Key Laboratory of Cryptology; China Electronic Technology Cyber Security Co., Ltd.; National Key Laboratory of Security Communication, Institute of Southwestern Communication; School of Cyberspace Security, Beijing University of Posts and Telecommunications（北京邮电大学网络与交换技术国家重点实验室; 密码学国家重点实验室; 中国电子科技集团网络安全有限公司; 西南通信研究所信息安全通信全国重点实验室; 北京邮电大学网络空间安全学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对FALQON深度高、SO-FALQON测量开销大的问题，提出BLS-FALQON方法，在保持低电路深度的同时减少测量次数，数值模拟和真实量子硬件实验均验证其有效性。
AI 中文摘要
反馈量子优化算法（FALQON）是一种用于求解组合优化问题的混合量子-经典算法，它绕过了经典参数优化，但需要较深的量子电路。为降低电路深度，Arai等人提出了二阶FALQON（SO-FALQON），在现有方法中实现了最佳的深度缩减。然而，SO-FALQON需要计算额外的二阶控制系数，导致每步测量开销增加2.3倍。本文受回溯线搜索（BLS）理论启发，提出了另一种方法BLS-FALQON，它不仅将电路深度缩减到与SO-FALQON相当的程度，而且实现了比SO-FALQON更少的测量次数。针对8至20个顶点的最大割问题的数值模拟表明，与SO-FALQON相比，BLS-FALQON将总测量次数减少了37.7%，同时保持了相当的电路深度。此外，我们在天衍-176量子计算机（使用祖冲之二号超导量子处理器）上进行了真实量子硬件实验，证实BLS-FALQON在真实量子硬件条件下仍然有效。
英文摘要
Feedback-based ALgorithm for Quantum OptimizatioN (FALQON) is a hybrid quantum-classical algorithm for solving combinatorial optimization problems, which circumvents classical parameter optimization but requires a deep quantum circuit. To reduce circuit depth, Arai et al. proposed second-order FALQON (SO-FALQON), achieving the best depth reduction among existing approaches. However, SO-FALQON brings a 2.3 times per-step measurement overhead, as it needs to calculate an additional second-order control coefficient. In this paper, inspired by the Backtracking Line Search (BLS) theory, we propose another method called BLS-FALQON, which not only reduces circuit depth to a comparable extent, but also achieves fewer measurements than SO-FALQON. Numerical simulations on max-cut problem with 8 to 20 vertices demonstrate that BLS-FALQON reduces the total measurement count by 37.7% compared to SO-FALQON, while maintaining a comparable circuit depth. Furthermore, we conduct real quantum hardware experiments on the Tianyan-176 quantum computer, which uses the zuchongzhi2 superconducting quantum processor, confirming that BLS-FALQON remains effective under real quantum hardware conditions.
Comments16 pages, 4 figures
