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

TL;DR

This paper compares two-qubit and multi-qubit gates within the toric code for quantum error correction, showing multi-qubit gates can significantly improve fault tolerance in trapped ion systems.

Contribution

It demonstrates that five-qubit gates outperform two-qubit gates in fault tolerance thresholds within the toric code, highlighting the benefits of multi-qubit gates for QEC.

Findings

Five-qubit gates improve fault tolerance threshold by approximately 40%.

Multi-qubit gates reduce circuit depth in stabilizer measurements.

Results are based on trapped ion qubits with photon scattering errors.

Abstract

In some quantum computing (QC) 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 multi-qubit 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{\o}lmer-S{\o}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 multi-qubit gates in the context of QEC.