Superconducting quantum circuit of NOR in quantum annealing.

The applicability of quantum annealing to various problems can be improved by expressing the Hamiltonian using a circuit satisfiability problem. We investigate the detailed characteristics of the NOR/NAND functions of a superconducting quantum circuit, which are the basic building blocks to implementing various types of problem Hamiltonians. The circuit is composed of superconducting flux qubits with all-to-all connectivity, where direct magnetic couplers are utilized instead of the variable couplers in the conventional superconducting quantum circuit.

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.

Bifurcation phenomenon in spin relaxation.

Spin relaxation in a strong-coupling regime (with respect to the spin system) is investigated in detail based on the spin-boson model in a stochastic limit. We find a bifurcation phenomenon in temperature dependence of relaxation constants, which is never observed in the weak-coupling regime. We also discuss inequalities among the relaxation constants in our model and show the well-known relation 2gamma(T)>or=gamma(L), for example, for a wider parameter region than before.