  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.
