Fraxonium: Fractional fluxon states for qudit encoding

TL;DR

This paper introduces a superconducting circuit that hosts fractional fluxon states, called fraxons, forming a protected qudit system with potential for advanced quantum computing applications.

Contribution

It generalizes fluxonium to create a multi-level qudit system using engineered Josephson potentials and proposes a protocol for single-qutrit gates.

Findings

Spectrum analysis for d=4 and d=5 qudits

Detailed study of the qutrit case

Proposed STIRAP protocol for single-qutrit gates

Abstract

We propose a superconducting circuit hosting $d$ low-lying states, well separated from the rest of the spectrum, that naturally realizes a qudit system protected from leakage errors. The system represents a generalization of the fluxonium and the low-energy states are constituted by fractional fluxon states, that we call {\it fraxons}, localized in the minima of a suitably designed Josephson potential. The latter is tailored through a Fourier engineering approach, that employs multi-harmonic Josephson building block elements composed by a Josephson junction and an inductance connected in series. We present the spectrum of a $d=4$ and a $d=5$ qudit system and study in detail the qutrit case. We analyze the dipole matrix elements for coupling to radiation and propose a non-Abelian, stimulated Raman adiabatic passage (STIRAP) protocol for single-qutrit gates, that is particularly suited for the present system. The proposed platform opens novel perspectives in circuit engineering and quantum computing beyond the qubit paradigm.