Quantum state transport in square lattice superconducting qubit circuits under gauge potential

In this paper, we study the transport properties of quantum states in square-lattice bit model by using inductive couplers to generate artificial gauge potential (effective magnetic flux). It is found theoretical calculation that eigenstates single particle and hole have same eigen energy spectrum, average currents, sinusoidally modulated effective flux, are opposite each other with respect energy. For an initial single-particle or single-hole state where only one lattice site occuplied, if time-inversion symmetry preserved (the flux integral multiple 4π), components time-dependent wave functions equal, otherwise they not equal. The analysis demonstrates above results due fact particle-hole operation for system Hamiltonian equivalent time inversion. addition, it when π, a transported between two adjacent bits, 0, diagonal through then reverse. Regardless value both share (particle hole) current occupation probability.