Coherence and decoherence in generalized and noisy Shor's algorithm
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911599619473408 |
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| author | Ye, Linlin Wu, Zhaoqi Zhou, Nanrun |
| author_facet | Ye, Linlin Wu, Zhaoqi Zhou, Nanrun |
| contents | Quantum coherence constitutes a fundamental physical mechanism essential to the study of quantum algorithms. We study the coherence and decoherence in generalized Shor's algorithm where the register $A$ is initialized in arbitrary pure state, or the combined register $AB$ is initialized in any pseudo-pure state, which encompasses the standard Shor's algorithm as a special case. We derive both the lower and upper bounds on the performance of the generalized Shor's algorithm, and establish the relation between the probability of calculating $r$ when the register $AB$ is initialized in any pseudo-pure state and the one when the register $A$ initialized in arbitrary pure state. Moreover, we study the coherence and decoherence in noisy Shor's algorithm and give the lower bound of the probability that we can calculate $r$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11962 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coherence and decoherence in generalized and noisy Shor's algorithm Ye, Linlin Wu, Zhaoqi Zhou, Nanrun Quantum Physics Quantum coherence constitutes a fundamental physical mechanism essential to the study of quantum algorithms. We study the coherence and decoherence in generalized Shor's algorithm where the register $A$ is initialized in arbitrary pure state, or the combined register $AB$ is initialized in any pseudo-pure state, which encompasses the standard Shor's algorithm as a special case. We derive both the lower and upper bounds on the performance of the generalized Shor's algorithm, and establish the relation between the probability of calculating $r$ when the register $AB$ is initialized in any pseudo-pure state and the one when the register $A$ initialized in arbitrary pure state. Moreover, we study the coherence and decoherence in noisy Shor's algorithm and give the lower bound of the probability that we can calculate $r$. |
| title | Coherence and decoherence in generalized and noisy Shor's algorithm |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2508.11962 |