Quantum Error Correction with magnetic molecules

TL;DR

This paper explores the potential of magnetic molecules with exchange-coupled metal ions to serve as multi-qubit systems for quantum error correction, challenging the assumption of independent spin qubits in solid-state quantum computing.

Contribution

It demonstrates how certain magnetic molecules can encode multiple qubits and analyzes their suitability for implementing quantum error correction codes like Shor's code.

Findings

The spectrum of specific magnetic molecules can encode nine qubits.

Relations between spin states and qubit states are established for certain molecules.

Potential molecular systems for experimental realization are discussed.

Abstract

Quantum algorithms often assume independent spin qubits to produce trivial $|\uparrow\rangle=|0\rangle$, $|\downarrow\rangle=|1\rangle$ mappings. This can be unrealistic in many solid-state implementations with sizeable magnetic interactions. Here we show that the lower part of the spectrum of a molecule containing three exchange-coupled metal ions with $S=1/2$ and $I=1/2$ is equivalent to nine electron-nuclear qubits. We derive the relation between spin states and qubit states in reasonable parameter ranges for the rare earth $^{159}$Tb$^{3+}$ and for the transition metal Cu$^{2+}$, and study the possibility to implement Shor's Quantum Error Correction code on such a molecule. We also discuss recently developed molecular systems that could be adequate from an experimental point of view.