Controllable Coupling in Phase-Coupled Flux Qubits

We propose a scheme for tunable coupling of phase-coupled flux qubits. The phase-coupling scheme can provide a strong coupling strength of the order of Josephson coupling energy of Josephson junctions in the connecting loop, while the previously studied inductive coupling scheme cannot provide due to small mutual inductance and induced currents. We show that, in order to control the coupling, we need {\it two} dc-SQUID's in the connecting loop and the control fluxes threading the dc-SQUID's must be in {\it opposite} directions. The coupling strength is analytically calculated as a function of the control flux at the co-resonance point.