External current as a coupler between the spin-vortex-induced loop current qubits

Abstract

The spin-vortex-induced loop current (SVILC) is a nano-sized loop current predicted to exist in the CuO2 plane in the bulk of hole-doped cuprate superconductors. It is a persistent loop current protected by the topological winding number associated with the wave function. It exists around a spin-vortex created by the itinerant electrons with a doped hole at its center. The direction of each SVILC can be either clockwise (winding number −1) or counterclockwise (winding number +1); and the currentless winding number zero is forbidden by the single-valued requirement of the wave function with respect to the electron coordinates. Recently, it has been demonstrated, theoretically, that this degree-of-freedom can be used for qubits. The gate-operation time by the Rabi oscillation using an electromagnetic field with electric field intensity 105 V m–1 is estimated to be several nanoseconds. This is comparable or shorter than the existing superconducting qubits. Since SVILCs do not require Cooper pairs, the SVILC qubit is free from the relaxation caused by broken Cooper pair electrons that is speculated to limit the qubit coherence time in the existing superconducting qubits. Thus, the coherence time for the SVILC qubit may exceed the value achieved by the superconducting qubit (about 100 μs). Further, since the stabilization temperature of SVILCs is expected to be the superconducting transition temperature of the cuprates, a much higher operation temperature may be possible for the SVILC qubits compared to the existing superconducting qubits, which requires the operation temperature of about 10 mK. In the present work, we show, theoretically, that coupling of two SVILC qubits can be achieved by external current feeding. This enables the construction of nano-sized qubit-couplers, and may provide a scalability that is needed in the construction of a fully fault-tolerant quantum computer.