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

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 Mølmer-Sørensen 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.

9 pages, 6 figures; updated simulation for five-qubit model, figures 5 and 6

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Cited by in corpus (7)

• Noisy intermediate-scale quantum computers
• Quantum Error Correction with Metastable States of Trapped Ions Using Erasure Conversion
• One Gate Scheme to Rule Them All: Introducing a Complex Yet Reduced Instruction Set for Quantum Computing
• The fastest generation of multipartite entanglement with natural interactions
• Modeling error correction with Lindblad dynamics and approximate channels
• Fault-Tolerant Stabilizer Measurements in Surface Codes with Three-Qubit Gates
• Multi-Mode Global Driving of Trapped Ions for Quantum Circuit Synthesis