Feedback-based quantum optimization with low depth and measurement
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.
Related
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- Depth analysis of the Quantum Approximate Optimization Algorithm with a Grover mixer
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BibTeX
@misc{huang2026feedbackbased,
title = {{Feedback-based quantum optimization with low depth and measurement}},
author = {Zi-Wen Huang and Jia-Cheng Fan and Xiao-Hui Ni and Su-Juan Qin and Xiao-Kai Hou and Wei Huang and Bing-Jie Xu and Fei Gao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32433},
eprint = {2609.32433},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32433},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Feedback-based quantum optimization with low depth and measurement
AU - Zi-Wen Huang
AU - Jia-Cheng Fan
AU - Xiao-Hui Ni
AU - Su-Juan Qin
AU - Xiao-Kai Hou
AU - Wei Huang
AU - Bing-Jie Xu
AU - Fei Gao
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32433
UR - https://arxiv.org/abs/2609.32433
AB - 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.
ER -