  Experimental demonstrations of quantum annealing with native implementation
of Boolean logic Hamiltonians are reported. 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. As examples of the truth table, NAND and NOR are successfully
fabricated as an identical circuit. Similarly, a native implementation of a
multiplier comprising six superconducting flux qubits is also demonstrated.
These native implementations of Hamiltonians consistent with Boolean logic
provide an efficient and scalable way of applying annealing computation to
so-called circuit satisfiability problems that aim to find a set of inputs
consistent with a given output over any Boolean logic functions, especially
those like factorization through a multiplier Hamiltonian. A proof-of-concept
demonstration of a hybrid computing architecture for domain-specific quantum
computing is described.
