A quantum processor is operable as a universal adiabatic quantum computing system. The quantum processor includes physical qubits, with at least a first and second communicative coupling available between pairs of qubits via an in-situ tunable superconducting capacitive coupler and an in-situ tunable superconducting inductive coupler, respectively. Tunable couplers provide diagonal and off-diagonal coupling. Compound Josephson junctions (CJJs) of the tunable couplers are responsive to a flux bias to tune a sign and magnitude of a sum of a capacitance of a fixed capacitor and a tunable capacitance which is mediated across a pair of coupling capacitors. The qubits may be hybrid qubits, operable in a flux regime or a charge regime. Qubits may include a pair of CJJs that interrupt a loop of material and which are separated by an island of superconducting material which is voltage biased with respect to a qubit body.