Factorization by quantum annealing using superconducting flux qubits implementing a multiplier Hamiltonian

Prime factorization (P = M × N) is a promising application for quantum computing. Shor's algorithm is a key concept for breaking the limit for analyzing P, which cannot be effectively solved by classical computation; however, the algorithm requires error-correctable logical qubits. Here, we describe a quantum annealing method for solving prime factorization. A superconducting quantum circuit with native implementation of the multiplier Hamiltonian provides combinations of M and N as a solution for number P after annealing. This circuit is robust and can be expanded easily to scale up the analysis. We present an experimental and theoretical exploration of the multiplier unit. We demonstrate the 2-bit factorization in a circuit simulation and experimentally at 10 mK. We also explain how the current conditions can be used to obtain high success probability and all candidate factorized elements.