Bayesian phase difference estimation based on single-photon projective measurement

doi:10.1088/1674-1056/adde33

中国物理B ›› 2025, Vol. 34 ›› Issue (7): 70305-070305.doi: 10.1088/1674-1056/adde33

Bayesian phase difference estimation based on single-photon projective measurement

Xu-Hao Yu(余旭豪)†, Ying Wei(韦颖)†, Ran Yang(杨然), Wen-Hui Song(宋文慧), Yingning Miao(缪应宁), Wei Zhou(周唯), Xinhui Li(李新慧), Xiaoqin Gao(高小钦), Yan-Xiao Gong(龚彦晓)‡, and Shi-Ning Zhu(祝世宁)

National Laboratory of Solid State Microstructures, School of Physics, Jiangsu Physical Science Research Center, and Collaborative Innovation Center of Advanced Microstructure, Nanjing University, Nanjing 210093, China

收稿日期:2025-05-05 修回日期:2025-05-29 接受日期:2025-05-29 出版日期:2025-06-18 发布日期:2025-07-03
通讯作者: Yan-Xiao Gong E-mail:gongyanxiao@nju.edu.cn
基金资助:
Project supported by the Natural Science Foundation of Jiangsu Province (Grant Nos. BK20233001 and BK20243060) and the National Natural Science Foundation of China (Grant No. 62288101).

Bayesian phase difference estimation based on single-photon projective measurement

National Laboratory of Solid State Microstructures, School of Physics, Jiangsu Physical Science Research Center, and Collaborative Innovation Center of Advanced Microstructure, Nanjing University, Nanjing 210093, China

Received:2025-05-05 Revised:2025-05-29 Accepted:2025-05-29 Online:2025-06-18 Published:2025-07-03
Contact: Yan-Xiao Gong E-mail:gongyanxiao@nju.edu.cn
Supported by:
Project supported by the Natural Science Foundation of Jiangsu Province (Grant Nos. BK20233001 and BK20243060) and the National Natural Science Foundation of China (Grant No. 62288101).

摘要/Abstract

摘要： The estimation of quantum phase differences plays an important role in quantum simulation and quantum computation, yet existing quantum phase estimation algorithms face critical limitations in noisy intermediate-scale quantum (NISQ) devices due to their excessive depth and circuit complexity. We demonstrate a high-precision phase difference estimation protocol based on the Bayesian phase difference estimation algorithm and single-photon projective measurement. The iterative framework of the algorithm, combined with the independence from controlled unitary operations, inherently mitigates circuit depth and complexity limitations. Through an experimental realization on the photonic system, we demonstrate high-precision estimation of diverse phase differences, showing root-mean-square errors (RMSE) below the standard quantum limit $\mathcal{O}(1/\sqrt{N})$ and reaching the Heisenberg scaling $\mathcal{O}(1/N)$ after a certain number of iterations. Our scheme provides a critical advantage in quantum resource-constrained scenarios, and advances practical implementations of quantum information tasks under realistic hardware constraints.

关键词: Bayesian phase difference estimation, single-photon projection measurement, Heisenberg limit, quantum information, quantum state engineering and measurements

Abstract: The estimation of quantum phase differences plays an important role in quantum simulation and quantum computation, yet existing quantum phase estimation algorithms face critical limitations in noisy intermediate-scale quantum (NISQ) devices due to their excessive depth and circuit complexity. We demonstrate a high-precision phase difference estimation protocol based on the Bayesian phase difference estimation algorithm and single-photon projective measurement. The iterative framework of the algorithm, combined with the independence from controlled unitary operations, inherently mitigates circuit depth and complexity limitations. Through an experimental realization on the photonic system, we demonstrate high-precision estimation of diverse phase differences, showing root-mean-square errors (RMSE) below the standard quantum limit $\mathcal{O}(1/\sqrt{N})$ and reaching the Heisenberg scaling $\mathcal{O}(1/N)$ after a certain number of iterations. Our scheme provides a critical advantage in quantum resource-constrained scenarios, and advances practical implementations of quantum information tasks under realistic hardware constraints.

Key words: Bayesian phase difference estimation, single-photon projection measurement, Heisenberg limit, quantum information, quantum state engineering and measurements

中图分类号: (Quantum computation architectures and implementations)

03.67.Lx

03.67.Ac (Quantum algorithms, protocols, and simulations) 42.50.Dv (Quantum state engineering and measurements) 03.67.Ac (Quantum algorithms, protocols, and simulations)

Xu-Hao Yu(余旭豪), Ying Wei(韦颖), Ran Yang(杨然), Wen-Hui Song(宋文慧), Yingning Miao(缪应宁), Wei Zhou(周唯), Xinhui Li(李新慧), Xiaoqin Gao(高小钦), Yan-Xiao Gong(龚彦晓), and Shi-Ning Zhu(祝世宁). Bayesian phase difference estimation based on single-photon projective measurement[J]. 中国物理B, 2025, 34(7): 70305-070305.

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Bayesian phase difference estimation based on single-photon projective measurement

Bayesian phase difference estimation based on single-photon projective measurement

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