Berry's phase in the Josephson phase qubit

TL;DR

This paper derives and analyzes Berry's phase in a Josephson phase qubit, exploring its potential for topological quantum computing by comparing geometric and Berry phases in a superconducting qubit system.

Contribution

It provides an alternative derivation of Berry's phase in a Josephson phase qubit and investigates its implications for topological quantum computing.

Findings

Calculated Berry's phase over a closed loop in frequency space

Compared Berry's phase with geometric phase

Discussed potential for topological quantum computing

Abstract

Berry's phase often appears in quantum two-level systems with a degeneracy. An example of such a system is a spin-1/2 particle in a magnetic field. As the magnetic field is slowly evolved through a closed path, the particle has been shown to acquire an additional phase called Berry's phase, in addition to the usual dynamical phase. This phase has been found in two-level quantum systems intrinsic to many superconducting qubits and has particularly been calculated for the charge, flux and Josephson phase qubit. Here, we present an alternative derivation of the Berry's phase in a current-biased Josephson junction qubit. We also calculate the complete Berry's phase evaluated over a closed loop in a frequency parameter space and compare this with the geometric phase. From this comparison, we examine the possibility of using a single phase qubit for topological quantum computing.