Multi-qudit interactions in molecular spins

TL;DR

This paper investigates photon-mediated interactions between molecular spin qudits, deriving effective models and analyzing their dynamics to facilitate quantum gate implementation in multi-level spin systems.

Contribution

It introduces a microscopic model for multi-qudit interactions including anisotropy and multi-level effects, and analyzes their dynamics for quantum gate design.

Findings

Derived effective interaction models for molecular spin qudits.

Calculated long-term dynamics for spin pairs using multiple scales analysis.

Identified 2-qudit gates and their implementation times.

Abstract

We study photon-mediated interactions between molecular spin qudits in the dispersive regime of operation. We derive from a microscopic model the effective interaction between molecular spins, including their crystal field anisotropy (i.e., the presence of non-linear spin terms) and their multi-level structure. Finally, we calculate the long time dynamics for a pair of interacting molecular spins using the method of multiple scales analysis. This allows to find the set of 2-qudit gates that can be realized for a specific choice of molecular spins and to determine the time required for their implementation. Our results are relevant for the implementation of logical gates in general systems of qudits with unequally spaced levels or to determine an adequate computational subspace to encode and process the information.