Unconditional correctness of recent quantum algorithms for factoring and computing discrete logarithms

ePrint Report: Unconditional correctness of recent quantum algorithms for factoring and computing discrete logarithms

Cédric Pilatte

In 1994, Shor introduced his famous quantum algorithm to factor integers and compute discrete logarithms in polynomial time. In 2023, Regev proposed a multi-dimensional version of Shor's algorithm that requires far fewer quantum gates. His algorithm relies on a number-theoretic conjecture on the elements in $(\mathbb{Z}/N\mathbb{Z})^{\times}$ that can be written as short products of very small prime numbers. We prove a version of this …

algorithm algorithms compute computing correctness eprint report factor factoring far logarithms quantum quantum algorithms report shor version