Circuit design implementing longitudinal coupling: a scalable scheme for superconducting qubits

TL;DR

This paper introduces a scalable superconducting qubit circuit design utilizing longitudinal coupling, enabling local interactions and simplified control for quantum computing applications.

Contribution

It proposes a novel fixed-frequency superconducting qubit circuit with longitudinal coupling, scalable to a grid with local interactions and minimal frequency requirements.

Findings

Implementing longitudinal coupling differs from traditional transverse coupling.

Scalability achieved with only four resonator frequencies and one qubit frequency.

Controlled phase gates can be performed without disturbing other qubits.

Abstract

We present a circuit construction for a new fixed-frequency superconducting qubit and show how it can be scaled up to a grid with strictly local interactions. The circuit QED realization we propose implements $\sigma_z$-type coupling between a superconducting qubit and any number of $LC$ resonators. The resulting \textit{longitudinal coupling} is inherently different from the usual $\sigma_x$-type \textit{transverse coupling}, which is the one that has been most commonly used for superconducting qubits. In a grid of fixed-frequency qubits and resonators with a particular pattern of always-on interactions, coupling is strictly confined to nearest and next-nearest neighbor resonators; there is never any direct qubit-qubit coupling. We note that just four distinct resonator frequencies, and only a single unique qubit frequency, suffice for the scalability of this scheme. A controlled phase gate between two neighboring qubits can be realized with microwave drives on the qubits, without affecting the other qubits. This fact is a supreme advantage for the scalability of this scheme.