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Prime factorization (P = M*N) is considered to be a promising application inquantum computations. We perform 4-bit factorization in experiments using asuperconducting flux qubit toward quantum annealing. Our proposed method uses asuperconducting quantum circuit implementing a multiplier Hamiltonian, whichprovides combinations of M and N as a factorization solution after quantumannealing when the integer P is initially set. The circuit comprises multiplemultiplier units combined with connection qubits. The key points are a nativeimplementation of the multiplier Hamiltonian to the superconducting quantumcircuit and its fabrication using a Nb multilayer process with a Josephsonjunction dedicated to the qubit. The 4-bit factorization circuit comprises 32superconducting flux qubits. Our method has superior scalability because theHamiltonian is implemented with fewer qubits than in conventional methods usinga chimera graph architecture. We perform experiments at 10 mK to clarify thevalidity of interconnections of a multiplier unit using qubits. We demonstrateexperiments at 4.2 K and simulations for the factorization of integers 4, 6,and 9.

4-bit Factorization Circuit Composed of Multiplier Units with Superconducting Flux Qubits toward Quantum Annealing