Precise Time Evolution of Superconductive Phase Qubits

New procedure on precise analysis of superconducting phase qubits using the concept of Feynman path integral in quantum mechanics and quantum field theory has been introduced. The wave function and imaginary part of the energy of the pseudo ground state of the Hamiltonian in phase qubits has been obtained from semi classical approximation and we we estimate decay rate, and thus the life time of meta stable using the approach of Instanton model. We devote the main effort to study the evolution of spectrum of Hamiltonian in time after addition of interaction Hamiltonian, in order to obtain the high fidelity quantum gates.