Ultrastrong capacitive coupling of flux qubits

TL;DR

This paper analyzes ultrastrong capacitive coupling in flux qubits, revealing complex interactions including non-stoquastic terms, and provides a comprehensive theoretical framework based on circuit parameters.

Contribution

It introduces a detailed theory for ultrastrong capacitive coupling in flux qubits, accounting for all interaction terms and their dependence on circuit properties.

Findings

Dominant $\sigma^y(a+a^^)$ coupling with LC resonators.

Complex non-stoquastic interactions in coupled flux qubits.

Theory applicable to various circuit designs and parameters.

Abstract

A flux qubit can interact strongly when it is capacitively coupled to other circuit elements. This interaction can be separated in two parts, one acting on the qubit subspaces and one in which excited states mediate the interaction. The first term dominates the interaction between the flux qubit and an LC-resonator, leading to ultrastrong couplings of the form $\sigma^y(a+a^\dagger),$ which complement the inductive $\sigma^xi(a^\dagger-a)$ coupling. However, when coupling two flux qubits capacitively, all terms need to be taken into account, leading to complex non-stoquastic ultrastrong interaction of the $\sigma^y\sigma^y$, $\sigma^z\sigma^z$ and $\sigma^x\sigma^x$ type. Our theory explains all these interactions, describing them in terms of general circuit properties---coupling capacitances, qubit gaps, inductive, Josephson and capactive energies---, that apply to a wide variety of circuits and flux qubit designs.