We propose and theoretically investigate spin superconducting qubits. Spin superconducting qubit consists of a single spin confined in a Josephson junction. We show that owing to spin-orbit interaction, superconducting 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 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. Spin superconducting 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.
