Theoretical proposal for superconducting spin qubits

We propose and theoretically investigate superconducting spin qubits. Superconducting spin qubit consists of a single spin confined in a Josephson junction. We show that owing to spin-orbit interaction, superconducting phase difference across the junction can polarize this spin. We demonstrate that this enables single-qubit operations and more complicated quantum gates, where spins of different qubits interact via a mutual inductance of the superconducting loop where the junctions are embedded. Recent experimental realizations of Josephson junctions made of semiconductor quantum dots in contact with superconducting leads have shown that the number of electrons in the quantum dot can be tuned by a gate voltage. Superconducting spin qubit is realized when the number of electrons is odd. We discuss the qubit properties at phenomenological level. We present a microscopic theory that enables us to make accurate estimations of the qubit parameters by evaluating the spin-dependent Josephson energy in the framework of fourth-order perturbation theory.