Quantization of Three-junction Superconducting Flux Quantum Bit System

Abstract

This work is aimed to present a method for the quantization of a many superconducting circuits coupling system. On the basis of rf-SQUID qubit, three Josephson junctions are connected in series in the superconducting loop to reduce the impact of the external electromagnetic environment on the bit. When there is an external magnetic flux in the superconducting ring, the Hamiltonian of the three-junction flux quantum bit is achieved. Firstly, ignoring the energy term caused by the applied potential in the kinetic energy term. Then the Lagrangian of the three-junction flux quantum bit is obtained by the Josephson junction characterization kinetic energy term. Secondly, canonical momentum is introduced to get the relationship of Hamiltonian potential energy. Finally, the potential energy is divided into two parts: the inherent potential energy of the system and the interaction energy of the system. Then, the Hamiltonian is discussed separately with additional time-dependent flux and no external flux.