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 wavefunction 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.
We propose a similarity between the scenario of fate of false vacuum in cosmology at early universe and the situation in where the quantum state decays in superconducting Flux qubit.This is due to the fact that both cases have two homogeneous stable equilibrium states in scalar field, which in quantum theory, could penetrate through the barrier in different possibilities and hence considered unstable decaying in time. In quantum computation, decay rate is among the most important factors in characteristics of the system like coherency, reliability, measurement fidelity, etc. In this considered potential, the decay rate from the penetrating (False vacuum) state to the stable (absolute minimum) state is achieved to leading order in Planck constant by the approach of Instanton model. In case of the superconducting flux qubit having thin barrier potential, the decay rate is calculated and its relations with actual set of parameters in flux qubit design are introduced.
In this paper we introduce a new procedure on precise analysis of various physical manifestations in superconducting Qubits using the concept of Feynman path integral in quantum mechanicsand quantum field theory. Three specific problem are discussed, we devote the main efforts to studying the wave function and imaginary part of the energy of the pseudo ground state of the Hamiltonian in Phase Qubits and we estimate decay rate, and thus the life time of meta stable states using the approach of ‚t Hooft’s Instantons model. Correction to the Tilted-Washboard potential and current of Phase Qubits by precise analysis of Ginzburg-Landau’s free energy equation has been considered. Also we evaluate the most accurate value of energy levels and wave function in Charge and Flux Qubits by Semi classical approximation in path integral formalism by considering limits of experimental errors, comparing them with WKB results and finally, we try to study more specific the evolution of spectrum of Hamiltonian in time after addition of interaction Hamiltonian, in order to obtain the high fidelity quantum gates.