The implementation of error correction protocols is a central challenge in the development of practical quantum information technologies. Recently, multi-level quantum resources such as harmonic oscillators and qudits have attracted interest in this context because they offer the possibility of additional Hilbert space dimensions in a spatially compact way. Here we propose a quantum memory, implemented on a spin-7/2 nucleus hyperfine-coupled to an electron spin-1/2 qubit, which provides first order X, Y and Z error correction using significantly fewer quantum resources than the equivalently effective qubit-based protocols. Our encoding may be efficiently implemented in existing experimentally realised molecular electron-nuclear quantum spin systems. The strategy can be extended to higher-order error protection on higher-spin nuclei.
@article{arxiv.2303.02084,
title = {Fault-tolerant qubit encoding using a spin-7/2 qudit},
author = {Sumin Lim and Junjie Liu and Arzhang Ardavan},
journal= {arXiv preprint arXiv:2303.02084},
year = {2023}
}