# M{\o}lmer-S{\o}rensen entangling gate for cavity QED systems

## TL;DR

This paper proposes a cavity QED implementation of the M{46}lmer-S{46}rensen entangling gate, utilizing cavity-assisted Raman transitions to achieve high-fidelity quantum entanglement, bridging techniques from ion traps to cavity QED systems.

## Contribution

It introduces a novel cavity QED-based entangling gate scheme inspired by ion trap methods, expanding the toolkit for quantum computing architectures.

## Key findings

- Proposed a cavity QED implementation of the M{46}lmer-S{46}rensen gate.
- Identified practical sources of infidelity affecting the gate.
- Discussed the transferability of techniques from ion traps to cavity QED.

## Abstract

The M{\o}lmer-S{\o}rensen gate is a state-of-the-art entangling gate in the ion trap quantum computing where the gate fidelity can exceed 99\%. Here we propose an analogous implementation in the setting of cavity QED. The cavity photon mode acts as the bosonic degree of freedom in the gate in contrast of that played by a phonon mode in ion traps. This is made possible by utilising cavity assisted Raman transitions interconnecting the logical qubit states embedded in a four-level energy structure, making the "anti-Jaynes-Cummings" (AJC) term available under the rotating-wave approximation. We identify practical sources of infidelity and discuss their effects on the gate performance. Our proposal not only demonstrates an alternative entangling gate scheme but also sheds new light on the relationship between ion traps and cavity QED, in the sense that many techniques developed in the former are transferable to the latter through our framework.