Developing Tools to Study Josephson Junction Arrays In New Regimes

Abstract

In this thesis, we study a class of superconducting circuits known as Josephson junction arrays with the goal of developing a set of numerical and analytic techniques to examine their viability as qubit systems. We study a specific case where the odd (black-sheep) junction has higher energy than the junction array (\(E_J^b \gg E_J^a\)), a regime that is opposite to that in which the fluxonium qubit resides, and remains largely unexplored. The spectrum of this system is highly degenerate, and we examine how this degeneracy forms and grows in the number of junctions in the array. We demonstrate the use of a novel numerical technique known as a \textit{spectral graph} that exploits the symmetry of the system to study its coherence times. Finally, we also do a perturbative calculation in small \(E_J^a\) and examine its accuracy.