  Quantum annealing (QA) is a heuristic algorithm for finding low-energy
configurations of a system, with applications in optimization, machine
learning, and quantum simulation. Up to now, all implementations of QA have
been limited to qubits coupled via a single degree of freedom. This gives rise
to a stoquastic Hamiltonian that has no sign problem in quantum Monte Carlo
(QMC) simulations. In this paper, we report implementation and measurements of
two superconducting flux qubits coupled via two canonically conjugate degrees
of freedom (charge and flux) to achieve a nonstoquastic Hamiltonian. Such
coupling can enhance performance of QA processors, extend the range of quantum
simulations. We perform microwave spectroscopy to extract circuit parameters
and show that the charge coupling manifests itself as a YY interaction in the
computational basis. We observe destructive interference in quantum coherent
oscillations between the computational basis states of the two-qubit system.
Finally, we show that the extracted Hamiltonian is nonstoquastic over a wide
range of parameters.
