Ultracold polar molecules as qudits

TL;DR

This paper explores how ultracold molecules can serve as multi-level quantum systems (qudits) for quantum computing, demonstrating a protocol for implementing the Deutsch algorithm using molecular states.

Contribution

It introduces a method to encode qudits in molecular internal states and proposes a protocol for quantum computation with these molecular qudits.

Findings

Identification of suitable molecular levels for 4-level qudits

Implementation of quantum gates via microwave transitions

Protocol for executing the Deutsch algorithm with molecular qudits

Abstract

We discuss how the internal structure of ultracold molecules, trapped in the motional ground state of optical tweezers, can be used to implement qudits. We explore the rotational, fine and hyperfine structure of $^{40}$Ca$^{19}$F and $^{87}$Rb$^{133}$Cs, which are examples of molecules with $^2\Sigma$ and $^1\Sigma$ electronic ground states, respectively. In each case we identify a subset of levels within a single rotational manifold suitable to implement a 4-level qudit. Quantum gates can be implemented using two-photon microwave transitions via levels in a neighboring rotational manifold. We discuss limitations to the usefulness of molecular qudits, arising from off-resonant excitation and decoherence. As an example, we present a protocol for using a molecular qudit of dimension $d=4$ to perform the Deutsch algorithm.