Feynman Path Integral Approach on Superconducting Qubits and Readout Process

TL;DR

This paper introduces a novel application of Feynman path integrals to analyze superconducting qubits, providing precise estimations of energy levels, decay rates, and wave functions to improve quantum gate fidelity.

Contribution

It presents a new method using Feynman path integrals for detailed analysis of superconducting qubits, including decay rates and energy corrections, advancing quantum computing research.

Findings

Estimated decay rates and lifetimes of metastable states.

Accurate energy levels and wave functions for Charge and Flux Qubits.

Analysis of Hamiltonian spectrum evolution for high-fidelity quantum gates.

Abstract

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 mechanics and 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.