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arXiv · 2609.32433

Feedback-based quantum optimization with low depth and measurement

Zi-Wen Huang·Jia-Cheng Fan·Xiao-Hui Ni·Su-Juan Qin·Xiao-Kai Hou·Wei Huang·Bing-Jie Xu·Fei Gao
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Abstract

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.

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Zi-Wen Huang, Jia-Cheng Fan, Xiao-Hui Ni, Su-Juan Qin, Xiao-Kai Hou, Wei Huang, Bing-Jie Xu, Fei Gao. 2026-09-26. Feedback-based quantum optimization with low depth and measurement. https://arxiv.org/abs/2609.32433

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