Quantum annealing with native implementation of Hamiltonian in the multiplier unit (MU) is experimentally demonstrated. As a superconducting integrated circuit, a problem Hamiltonian whose set of ground states is consistent with a given truth table is implemented for quantum annealing with no redundant qubits. In the MU, six qubits with all-to-all connectivity are utilized. Six qubits (X, Y, Z, D, C, S) correspond to the X and Y for inputs, Z and D for carry-in, C for carry-out, and S for summation. Hamiltonian of the MU take minimal energy in sixteen combinations of qubits (X, Y, Z, D, C, S). We define the external flux bias condition of the six qubits as a degeneracy point, where these combinations will appear. By applying offset currents to the qubits (X, Y, Z, D) at the degeneracy point, we can produce one of the logic elements of the multiplication after the quantum annealing. Similarly, the factorization is possible after the quantum annealing with adoption of appropriate offset currents to the qubits (C, S).
We fabricated the MU using superconducting integrated circuit technologies for superconducting flux qubits, providing Nb 4-layers and a Josephson junction with a critical current density Jc of 1 μA/μm2. The critical current Ic in the qubit was designed as 6.25 μA. Experiment was carried out at 10 mK using the dilution refrigerator. First, we found the degeneracy point by exploring the external flux bias with wide range. By applying the offset current to the degeneracy point, we confirmed the generation of all candidate elements in the multiplication. In addition, factorizations of 3(10) = (1,1)(2), 2(10) = (1,0)(2), 1(10) = (0,1)(2), 0(10) = (0,0)(2) were confirmed with above 80 % in success probabilities. Further, the behavior of the MU in the multiplication and the factorization were analytically confirmed by a Josephson circuit simulation. These results indicate the possibility of a scalable factorization circuit by assembling the MU.
Keywords: quantum annealing, superconducting flux qubit, factorization, multiplier