Quantum Factoring Algorithm using Grover Search

We present a quantum algorithm for factoring products of prime numbers which exploits Grover search to factor any \(n\)-bit biprime using \(2n-5\) qubits or less. The algorithm doesn't depend on any properties of the number to be factored, has guaranteed convergence, and doesn't require complex classical pre or post-processing. Large scale simulations confirm a success probability asymptotically reaching 100% for \(>800\) random biprimes with \(5\leq n\leq 35\) (corresponding to \(5 - 65\) qubits) with the largest being \(30398263859 = 7393\times 4111763\). We also present a variant of the algorithm based on digital adiabatic quantum computing and show that Grover based factorization requires quadratically fewer iteration steps in most cases.