  We consider how the Hamiltonian Quantum Computing scheme introduced in
[arXiv:1509.01278] can be implemented using a 2D array of superconducting
transmon qubits. We show how the scheme requires the engineering of strong
attractive cross-Kerr and weak flip-flop or hopping interactions and we detail
how this can be achieved. Our proposal uses a new electric circuit for
obtaining the attractive cross-Kerr coupling between transmons via a
dipole-like element. We discuss and numerically analyze the forward motion and
execution of the computation and its dependence on coupling strengths and their
variability. We extend [arXiv:1509.01278] by explicitly showing how to
construct a direct Toffoli gate, thus establishing computational universality
via the Hadamard and Toffoli gate or via controlled-Hadamard, Hadamard and
CNOT.
