Diffusion and transfer of entanglement in an array of inductively coupled flux qubits

A theoretical scheme to generate multipartite entangled states in a Josephson planar-designed architecture is reported. This scheme improves the one published by Migliore et al. [Phys. Rev. B 74, 104503 (2006)] since it speeds up the generation of $W$ entangled states in an $M\times N$ array of inductively coupled Josephson flux qubits by reducing the number of necessary steps. In addition, the same protocol is shown to be able to transfer the $W$ state from one row to the other.

Figure 1

Schematic illustration of an $M\times N$ array of Josephson flux qubits. An inductive qubit-qubit coupling is realized by means of a superconducting switch, namely, a transformer with variable flux-transfer function $\mathcal{R}\left({\varphi }_{cx}^{\left(mn\right)}\right)$, as proposed in Ref. 4. It is possible to control the flux-transfer function, and therefore the inductive-coupling constant, by modulating the critical current of the inner dc SQUID of each transformer via an externally applied magnetic flux ${\varphi }_{cx}^{\left(mn\right)}$. Each individual coupling between a pair of qubits is effectively turned on by adjusting the control fluxes of the relevant “switches” with all the other switches kept off.