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arXiv · 2405.20950

Quantum computation with hybrid parafermion-spin qubits

Denis V. Kurlov·Melina Luethi·Anatoliy I. Lotkov·Katharina Laubscher·Jelena Klinovaja·Daniel Loss
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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.

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Denis V. Kurlov, Melina Luethi, Anatoliy I. Lotkov, Katharina Laubscher, Jelena Klinovaja, Daniel Loss. 2024-05-31. Quantum computation with hybrid parafermion-spin qubits. https://doi.org/10.1103/7cd9-c7yc

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