  By coupling pairs of superconducting qubits through a small Josephson
junction with a time-dependent flux bias, we show that arbitrary interactions
involving any combination of Pauli matrices can be generated with a small
number of drive tones applied through the flux bias of the coupling junction.
We then demonstrate that similar (though not fully universal) results can be
achieved in capacitively coupled qubits by exploiting the higher energy states
of the devices through multi-photon drive signals applied to the qubits' flux
degrees of freedom. By using this mechanism to couple a qubit to a detuned
resonator, the qubit's rotating frame state can be non-destructively measured
along any direction on the Bloch sphere. Finally, we describe how the
frequency-converting nature of the couplings can be used to engineer a
mechanism analogous to dynamic nuclear polarization in NMR systems, capable of
cooling an array of qubits well below the ambient temperature, and outline how
higher order interactions, such as local 3-body terms, can be engineered
through the same couplings. Our results demonstrate that a programmable quantum
simulator for large classes of interacting spin models could be engineered with
the same physical hardware.
