Long range magnetic dipole-dipole interaction mediated by a superconductor

Quantum computation and simulation requires strong coherent coupling between qubits, which may be spatially separated. Achieving this coupling for solid-state based spin qubits is a long-standing challenge. Here we theoretically investigate a method for achieving such coupling, based on superconducting nano-structures designed to channel the magnetic flux created by the qubits. We detail semi-classical analytical calculations and simulations of the magnetic field created by a magnetic dipole, depicting the spin qubit, positioned directly below nanofabricated apertures in a superconducting layer. We show that such structures could channel the magnetic flux, enhancing the dipole-dipole interaction between spin qubits and changing its scaling with distance, thus potentially paving the way for controllably engineering an interacting spin system.