Robust encoding of a qubit in a molecule

TL;DR

This paper introduces quantum error-correcting codes utilizing the rotational states of molecules, enabling robust quantum information storage and processing in infinite-dimensional Hilbert spaces with potential applications in molecular and atomic systems.

Contribution

It develops new quantum error-correcting codes based on molecular rotational states, extending to systems with symmetry axes and nonabelian Lie groups, broadening quantum information encoding possibilities.

Findings

Codes protect against orientation drift and angular momentum changes

Extensions to diatomic molecules and nuclear states demonstrated

Framework for quantum processing on complex configuration spaces established

Abstract

We construct quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert state space of rotational states of a rigid body. These codes, which protect against both drift in the body's orientation and small changes in its angular momentum, may be well suited for robust storage and coherent processing of quantum information using rotational states of a polyatomic molecule. Extensions of such codes to rigid bodies with a symmetry axis are compatible with rotational states of diatomic molecules, as well as nuclear states of molecules and atoms. We also describe codes associated with general nonabelian compact Lie groups and develop orthogonality relations for coset spaces, laying the groundwork for quantum information processing with exotic configuration spaces.