Splitting of energy levels of Spin-vortex Induced Loop Currents by feeding external currents

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 is -1) or counterclockwise (winding number is +1) and the winding number with no current (winding number is zero) is forbidden by the singlevalued 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. Coupling of neighboring qubits by external current feeding is confirmed to be realizable. This means that nano-sized couplers of SVILC qubits using feeding external currents are realizable. The size of couplers of SVILC qubits can be conparable or smaller than that of trapped ion qubits. Couper size of SVILC qubits is decided by the range of spin vortices in CuO₂ plane and current distribution, thus, this is tunable by feeding external current and substituting Cu atoms in barrier atoms. That of trapped ion qubits is limited by the distance that combined vibration occurs or laser range with respect to the coordinates. In the present work, We demonstrated splitting energy levels by external feeding current of three qubit system of SVILC qubits. This means that nano-sized qubit differentiator can be realized, and noise by static magnetic field can be cut off, and this may enable the realizing fully-fault tolerant quantum computers by SVILC qubits. Moreover, the possibility of downscaling of them is shown.