Hamltonian Quantum Computing with transmon qubits

We discuss a possible implementation based on superconducting transmon qubits of the scheme for Hamiltonian
Quantum Computing introduced in Ref. [1]. The scheme is completely passive and requires active control only for
initialization and measurement. The scheme requires strong and negative cross-Kerr interactions and relatively weaker
hopping interactions. We propose the implementation the strong of the cross-Kerr interactions with a newly designed direct
coupler based on array of few Josephson junctions, which should allow to reach larger cross-Kerr coupling compared to
other proposals, without causing any increase in the problem of cross-talk. The hopping interactions are responsible
for the implementation of quantum gates, and can be implemented with simple capacitances or via indirect coupling
mediated by resonators. In this way it is possible to obtain sufficient flexibility to achieve universality using only real
gates. To this end, we also discuss explicitly how to implement a Toffoli gate. We finally discuss the main sources of
errors in the model.

[1] S. Lloyd and B. M. Terhal, “Adiabatic and hamiltonian computing on a 2d lattice with simple two-qubit interactions,” New
Journal of Physics, vol. 18, no. 2, p. 023042, 2016.