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Implementation And Analysis of Regev's Quantum Factorization Algorithm

delete2026-03-01
delete0
PRE
AI
P
Pawlitko, Przemyslaw
M
Mocko, Natalia
N
Niemiec, Marcin *
C
Cholda, Piotr
DOI：10.2478/qic-2026-0012delete
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Abstract

Abstract

En 中文
Quantum computing represents a significant advancement in computational capabilities. Of particular concern is its impact on asymmetric cryptography through, notably, Shor's algorithm and the more recently developed Regev's algorithm for factoring composite numbers. We present our implementation of the latter with the aim of exposing experimental phenomena. Our analysis encompasses both quantum simulation results and classical component examples, with particular emphasis on comparative cases between Regev's and Shor's algorithms. Our experimental results reveal that Regev's algorithm outperforms Shor's algorithm for certain composite numbers in practice. However, we observed significant performance variations across different input values. Despite Regev's algorithm's theoretical asymptotic advantage in effectiveness, our implementation exhibited longer execution times than Shor's algorithm for small-integer factorization in both quantum and classical components. These findings offer insights into the practical challenges and performance characteristics of implementing Regev's algorithm in realistic quantum computing scenarios.
Keywords:
factorization
quantum algorithms
quantum computers
Regev's algorithm
Shor's algorithm

Journal

Q
QUANTUM INFORMATION & COMPUTATION
IF:
0.8
Papers:
23
Citations:
0

Organization

No organization information available