Comparing two-qubit and multiqubit gates within the toric code

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