Quantization of the double-qubit structure and quantum computation

The quantization scheme of a double-qubit structure with superconducting quantum interference devices (SQUIDs) is given. By introducing unitary matrices and using spectral decompositions, the Hamiltonian operator of the system is exactly formulated in compact forms in spin-1/2 notation. A scheme of designing controlled-phase-shift (CPS) gates is also proposed by using this circuit system.