Mediated tunable coupling of flux qubits

It is sketched how a monostable rf- or dc-SQUID can mediate an inductive coupling between two adjacent flux qubits. The non-trivial dependence of the SQUID's susceptibility on external flux makes it possible to continuously tune the induced coupling from antiferromagnetic (AF) to ferromagnetic (FM). In particular, for suitable parameters, the induced FM coupling can be sufficiently large to overcome any possible direct AF inductive coupling between the qubits. The main features follow from a classical analysis of the multi-qubit potential. A fully quantum treatment yields similar results, but with a modified expression for the SQUID susceptibility. Since the latter is exact, it can also be used to evaluate the susceptibility - or, equivalently, energy-level curvature - of an isolated rf-SQUID for larger shielding and at degenerate flux bias, i.e., a (bistable) qubit. The result is compared to the standard two-level (pseudospin) treatment of the anticrossing, and the ensuing conclusions are verified numerically.