Quantum Physics

    

Shor’s Algorithm Base Range Reduction: Symmetry of Successful Bases

Authors: Muhammad Saad Bhatti

Shor’s algorithm factors large integers in polynomial time by reducing the problem to finding the order of a randomly chosen base modulo N. The algorithm succeeds when the chosen base a has an even order and avoids a trivial root of −1. In this paper, we prove a symmetry property: if a is a successful base for Shor’s algorithm, then so is N − a. This symmetry implies that successful bases always occur in pairs, allowing us to restrict the search range of bases to less than N/2 without loss of generality.

Comments: 2 Pages. (Note by viXra Admin: For the last time, Please cite listed scientific references)

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Submission history

[v1] 2025-10-02 23:27:20 (removed)
[v2] 2025-12-09 01:04:19

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