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Analog quantum simulations offer rich opportunities for exploring complexquantum systems and phenomena through the use of specially engineered,well-controlled quantum systems. A critical element, increasing the scope andflexibility of such experimental platforms, is the ability to access and tunein situ different interaction regimes. Here, we present a superconductingcircuit building block of two highly coherent transmons featuring in situtuneable photon hopping and nonlinear cross-Kerr couplings. The interactionsare mediated via a nonlinear coupler, consisting of a large capacitor inparallel with a tuneable superconducting quantum interference device (SQUID).We demonstrate the working principle by experimentally characterising thesystem in the single- and two-excitation manifolds, and derive a fulltheoretical model that accurately describes our measurements. Both qubits havehigh coherence properties, with typical relaxation times in the range of 15 to40 microseconds at all bias points of the coupler. Our device could be used asa scalable building block in analog quantum simulators of extended Bose-Hubbardand Heisenberg XXZ models, and may also have applications in quantum computingsuch as realising fast two-qubit gates and perfect state transfer protocols.

Tuneable hopping and nonlinear cross-Kerr interactions in a high-coherence superconducting circuit