Quantum computation with hybrid parafermion-spin qubits

TL;DR

This paper introduces a universal set of quantum gates for hybrid qubits combining quantum dot spins and parafermions, expanding quantum computing possibilities with new symmetry considerations and experimental implementations.

Contribution

It develops a formalism for hybrid parafermion-spin qubits using Fock parafermions and highlights the role of particle-hole symmetry, proposing experimental realizations for specific parafermion types.

Findings

Universal quantum gates for hybrid qubits are proposed.

Particle-hole symmetry is crucial in these systems.

Experimental schemes for $ ext{Z}_4$ and $ ext{Z}_6$ parafermions are outlined.

Abstract

We propose a universal set of single- and two-qubit quantum gates acting on a hybrid qubit formed by coupling a quantum dot spin qubit to a $\mathbb{Z}_{2m}$ parafermion qubit with arbitrary integer $m$. The special case $m=1$ reproduces the results previously derived for Majorana qubits. Our formalism utilizes Fock parafermions, facilitating a transparent treatment of hybrid parafermion-spin systems. Furthermore, we highlight the previously overlooked importance of particle-hole symmetry in these systems. We give concrete examples how the hybrid qubit system could be realized experimentally for $\mathbb{Z}_4$ and $\mathbb{Z}_6$ parafermions. In addition, we discuss a simple readout scheme for the fractional parafermion charge via the measurement of the spin qubit resonant frequency.