Quantum factorization algorithm by NMR ensemble computers

Abstract

In this paper, we design our quantum factorization algorithm by using NMR ensemble computers. Our algorithm can find the prime factor p of the RSA-modulus N = pq by using NMR ensemble search scheme, where p < N , p and q are primes. We prepare massive molecules with the same states and use an auxiliary spin to record the result of computing. In each computation, we input states with one fixed spin and determine one bit value of the prime factor p. After ⌈ln p⌉computations, we can discover the factor p. Thus, our algorithm requires at most ln N oracle queries for factoring the RSA-modulus N.