Theory of superconducting qubits beyond the lumped element approximation

TL;DR

This paper develops a new formalism for superconducting qubits that goes beyond the traditional lumped element model, allowing for non-perturbative treatment of Josephson couplings and providing insights into small device behaviors.

Contribution

It introduces a gauge transformation-based formalism that captures complex physical effects in superconducting qubits beyond standard approximations.

Findings

Fermi sea effects influence effective capacitance in small charge qubits.

Asymmetry observed in current states of small RF SQUIDs.

Microscopic wavefunction for superconducting Schrödinger cat states provided.

Abstract

In the design and investigation of superconducting qubits and related devices, a lumped element circuit model is the standard theoretical approach. However, many important physical questions lie beyond its scope, e.g. the behavior of circuits with strong Josephson junctions carrying substantial currents and the properties of small superconducting devices. By performing gauge transformations on self-consistent solutions of the Bogoliubov-de Gennes equations, we develop here a formalism that treats Josephson couplings non-perturbatively. We apply the formalism to (a) show that Fermi sea effects can contribute to the effective capacitance of small charge qubits; (b) demonstrate an asymmetry in clockwise and counterclockwise current states in small RF squid qubits; and (c) provide a microscopic wavefunction of superconducting Schrodinger cats suitable for computing the number of entangled electrons.