Comparing two-qubit and multiqubit gates within the toric code

In some quantum computing architectures, entanglement of an arbitrary number qubits can be generated in a single operation. This property has many potential applications, and may specifically useful for error correction (QEC). Stabilizer measurements then implemented using multiqubit gate instead several two-qubit gates, thus reducing circuit depth. this study, the toric code is used as benchmark to compare performance five-qubit gates within parity-check circuits. We consider trapped ion that are controlled via Raman transitions, where primary source assumed spontaneous photon scattering. show M\o{}lmer-S\o{}rensen offers approximately $40%$ improvement over terms fault tolerance threshold. result indicates advantage context QEC.