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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 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 |
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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 $r$.
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Received: 11 November 2025
Revised: 08 January 2026
Accepted manuscript online: 11 February 2026
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PACS:
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03.67.Ac
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(Quantum algorithms, protocols, and simulations)
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03.65.Yz
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(Decoherence; open systems; quantum statistical methods)
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03.67.-a
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(Quantum information)
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| Fund: 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). |
Corresponding Authors:
Zhaoqi Wu
E-mail: wuzhaoqi_conquer@163.com
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Cite this article:
Linlin Ye(叶琳琳), Zhaoqi Wu(吴照奇), and Nanrun Zhou(周南润) Coherence and decoherence in generalized Shor’s algorithm 2026 Chin. Phys. B 35 060304
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