# Doubly Nonlinear Superconducting Qubit

## TL;DR

This paper introduces a novel superconducting circuit combining a Josephson junction and a quantum phase slip wire, which realizes a Hamiltonian with potential for noise-insensitive qubit states through its unique eigenstructure.

## Contribution

It presents a new superconducting circuit design with a Hamiltonian periodic in charge and flux, enabling noise-insensitive qubit states at critical points.

## Key findings

- Hamiltonian exactly diagonalizable in a double-Bloch band
- Eigenstates form Gottesman-Kitaev-Preskill quantum error correcting code
- Eigenstates at critical points are insensitive to charge and flux noise

## Abstract

We describe a superconducting circuit consisting of a Josephson junction in parallel with a quantum phase slip wire, which implements a Hamiltonian that is periodic in both charge and flux. This Hamiltonian is exactly diagonalisable in a double-Bloch band, and the eigenstates are shown to be code states of the Gottesman-Kitaev-Preskill quantum error correcting code. The eigenspectrum has several critical points, where the linear sensitivity to external charge and flux noise vanishes. The states at these critical points thus hold promise as qubit states that are insensitive to external noise sources.