Demonstration of a non-stoquastic Hamiltonian in coupled superconducting flux qubits

Currently available quantum annealers (QA) provide solutions to the transverse field Ising model with thousands of magnetically coupled qubits. To achieve a non-stoquastic Hamiltonian with QA, coupling via two canonically conjugate (orthogonal) degrees of freedom is necessary. Furthermore this orthogonal coupling can potentially enhance the performance of QA processors and enable an extended range of quantum simulations. Here we present one- and two-qubit microwave spectroscopy as well as time evolution measurements on two superconducting flux qubits coupled via two orthogonal degrees of freedom, charge and flux. We show that the electrostatic interaction, realized through a coupling capacitor, produces \sigma_y\sigma_y coupling in the computational basis and leads to broken gauge invariance. We also observe emergence of \sigma_x\sigma_x coupling through higher energy states of each rf-SQUID. Finally, we show that the reduced two qubit Hamiltonian is nonstoquastic across a wide range of parameters.