Entropy-based framework for quantum algorithm 1 robustness: discriminating noise channel impacts on 2 Shor’s period finding and establishing critical 3 performance thresholds

Public-key cryptosystems such as RSA rely on the classical intractability of integer factorization, which is threatened by Shor’s quantum algorithm. While theoretically efficient, practical implementations face significant challenges due to noise in current quantum devices. This paper introduces an information-theoretic framework based on von Neumann entropy to analyze the robustness of Shor’s period-finding subroutine under various noise models. Through simulations of small moduli ( $$N=15,21$$ ) under depolarizing, amplitude damping, and phase damping channels, this study demonstrates that entropy growth strongly correlates with success probability degradation, identify critical entropy thresholds marking the collapse of period finding, and report a robustness hierarchy, amplitude damping > phase damping > depolarizing noise. These findings provide hardware-agnostic insights for cryptanalytic security assessment and error mitigation strategies.