Toward the detection of spin-vortex-induced loop currents in a single bilayer Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ thin film and their possible use as qubits: Model calculations for three nano-island architecture

A theory for cuprate superconductivity predicts the existence of nano-sized loop currents called, ``spin-vortex-induced loop currents (SVILCs)''. In this wok, we first calculate magnetic fields produced by them in a single bilayer Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212) thin film for the purpose of detecting the SVILCs. The estimated magnitude of the magnetic field at the point 10$a$ ($a$ is the lattice constant of the CuO$_2$ plane) above the surface could be in the order of 100mT; thus, they may be detectable by currently available detection methods. Next, we investigate the use of them as qubits (the ``SVILC qubits'') in an architecture composed of three nano-islands of the thin film; and consider the use of the detection of the magnetic field generated by the SVILCs as the qubit readout. We show there are a number of energy levels suitable for qubit states that can be manipulated by external current feeding, and the magnetic field generated by the SVILCs is large enough to be used for the readout.