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arXiv · 2505.00433

Success probability in Shor's Algorithm

Ali Abbassi·Lionel Bayle
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Abstract

This paper aims to determine the exact success probability at each step of Shor's algorithm. Although the literature usually provides a lower bound on this probability, we present an improved bound. The derived formulas enable the identification of all failure cases in Shor's algorithm, which correspond to a success probability of zero. A simulation routine is provided to evaluate the theoretical success probability for a given integer when its prime factorization is known with potential applications in quantum resource estimation and algorithm benchmarking.

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Ali Abbassi, Lionel Bayle. 2025-05-01. Success probability in Shor's Algorithm. https://arxiv.org/abs/2505.00433

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