中国物理B ›› 2026, Vol. 35 ›› Issue (6): 60304-060304.doi: 10.1088/1674-1056/ae445e

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Coherence and decoherence in generalized Shor’s algorithm

Linlin Ye(叶琳琳)1, Zhaoqi Wu(吴照奇)1,†, and Nanrun Zhou(周南润)2,3   

  1. 1 Department of Mathematics, Nanchang University, Nanchang 330031, China;
    2 School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China;
    3 Department of Electronic Information Engineering, Nanchang University, Nanchang 330031, China
  • 收稿日期:2025-11-11 修回日期:2026-01-08 接受日期:2026-02-11 发布日期:2026-06-15
  • 通讯作者: Zhaoqi Wu E-mail:wuzhaoqi_conquer@163.com
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12561084 and 12161056) and the Natural Science Foundation of Jiangxi Province, China (Grant No. 20232ACB211003).

Coherence and decoherence in generalized Shor’s algorithm

Linlin Ye(叶琳琳)1, Zhaoqi Wu(吴照奇)1,†, and Nanrun Zhou(周南润)2,3   

  1. 1 Department of Mathematics, Nanchang University, Nanchang 330031, China;
    2 School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China;
    3 Department of Electronic Information Engineering, Nanchang University, Nanchang 330031, China
  • Received:2025-11-11 Revised:2026-01-08 Accepted:2026-02-11 Published:2026-06-15
  • Contact: Zhaoqi Wu E-mail:wuzhaoqi_conquer@163.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12561084 and 12161056) and the Natural Science Foundation of Jiangxi Province, China (Grant No. 20232ACB211003).

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摘要： Quantum coherence constitutes a fundamental physical mechanism essential to the study of quantum algorithms. We study coherence and decoherence in the generalized Shor's algorithm where the register $A$ is initialized in an arbitrary pure state, or the combined register $AB$ is initialized in a pseudo-pure state, which encompasses the standard Shor's algorithm as a special case. We derive both lower and upper bounds on the performance of the generalized Shor's algorithm, and establish the relation between the probability of calculating the order $r$ when register $AB$ is initialized in a pseudo-pure state and that when register $A$ is initialized in an arbitrary pure state. Moreover, we study coherence and decoherence in the noisy Shor's algorithm and give a lower bound on the probability that we can calculate the order $r$.

关键词: Shor's algorithm, coherence, decoherence, success probability

Abstract: Quantum coherence constitutes a fundamental physical mechanism essential to the study of quantum algorithms. We study coherence and decoherence in the generalized Shor's algorithm where the register $A$ is initialized in an arbitrary pure state, or the combined register $AB$ is initialized in a pseudo-pure state, which encompasses the standard Shor's algorithm as a special case. We derive both lower and upper bounds on the performance of the generalized Shor's algorithm, and establish the relation between the probability of calculating the order $r$ when register $AB$ is initialized in a pseudo-pure state and that when register $A$ is initialized in an arbitrary pure state. Moreover, we study coherence and decoherence in the noisy Shor's algorithm and give a lower bound on the probability that we can calculate the order $r$.

Key words: Shor's algorithm, coherence, decoherence, success probability

中图分类号:  (Quantum algorithms, protocols, and simulations)

  • 03.67.Ac
03.65.Yz (Decoherence; open systems; quantum statistical methods) 03.67.-a (Quantum information)