Comparing Two-Qubit and Multi-Qubit Gates within the Toric Code

Quantum error correction (QEC) is a necessary component for any long-term realization of a quantum computer. So far, QEC works seem to consider only standard gate sets involving two-qubit entangling gates. However in several quantum computing architectures, such as trapped ion systems, it is possible to exceed this regime by entangling many qubits in a single operation. Stabilizer measurements can then be implemented using a single multi-qubit gate instead of several two-qubit gates.

We focus on the toric code, and study its performance when using either two-qubit or five-qubit gates [1]. While using five-qubit gates dramatically reduces the number of required operations, these gates may also be more susceptible to error. Because of this trade-off, it is hard to predict which method yields better results.

We simulate the toric code using both methods and extract the fault tolerance (FT) threshold in each case. We show that using five-qubit gates offers an approximately 40% improvement in the FT threshold over the standard two-qubit gate method. Moreover, the former gives a 3.7 times improvement in logical error rates at low physical error probabilities. These results indicate an advantage of using multi-qubit gates in the context of QEC.

 

 [1] D. Schwerdt et al. PRA (2022, accepted)