Fault-tolerant qubit encoding using a spin-7/2 qudit

TL;DR

This paper proposes a fault-tolerant quantum memory using a spin-7/2 qudit that enables first-order error correction with fewer resources, leveraging existing molecular spin systems for efficient implementation.

Contribution

It introduces a novel qubit encoding scheme using a spin-7/2 nucleus for efficient first-order error correction, extending the capabilities of quantum error correction in molecular spin systems.

Findings

First-order $X$, $Y$, $Z$ error correction demonstrated

Fewer quantum resources needed compared to qubit protocols

Compatible with existing molecular spin systems

Abstract

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.