The quantization of persistent current qubit. The role of inductance

TL;DR

This paper derives the Hamiltonian and current operator for persistent current qubits, highlighting the impact of finite inductance on flux basis measurements, which is crucial for coupled flux qubit circuits.

Contribution

It provides a self-consistent derivation of the current operator considering finite inductance, revealing non-diagonal elements in the flux basis.

Findings

Current operator is not diagonal in flux basis due to inductance.

Finite inductance introduces non-diagonal elements in the current operator.

Results are relevant for coupled flux qubit circuits.

Abstract

The Hamiltonian of persistent current qubit is found within well known quantum mechanical procedure. It allows a selfconsistent derivation of the current operator in a two state basis. It is shown that the current operator is not diagonal in a flux basis. A non diagonal element comes from the finite inductance of the qubit. The results obtained in the paper are important for the circuits where two or more flux qubits are coupled inductively.