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.

arXiv comment9 pages, 6 figures; updated simulation for five-qubit model, figures 5 and 6

References in corpus (32)

• Fault-tolerant quantum computation by anyons
• Surface codes: Towards practical large-scale quantum computation
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Topological quantum memory
• Multi-particle entanglement of hot trapped ions
• Entanglement and quantum computation with ions in thermal motion
• High-fidelity quantum logic gates using trapped-ion hyperfine qubits
• High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions
• High-Fidelity Universal Gate Set for ${}^9$Be${}^{+}$ Ion Qubits
• High threshold universal quantum computation on the surface code
• Quantum computing with nearest neighbor interactions and error rates over 1%
• Quantum Error Correction
• Towards practical classical processing for the surface code
• Quantum information processing with trapped ions
• Errors in trapped-ion quantum gates due to spontaneous photon scattering
• Assessing the progress of trapped-ion processors towards fault-tolerant quantum computation
• Scalable global entangling gates on arbitrary ion qubits
• Robust two-qubit gates in a linear ion crystal using a frequency-modulated driving force
• Fault-tolerant thresholds for quantum error correction with the surface code
• Basic circuit compilation techniques for an ion-trap quantum machine
• Hyperfine Coherence in the Presence of Spontaneous Photon Scattering
• Robust entanglement gates for trapped-ion qubits
• Efficient Arbitrary Simultaneously Entangling Gates on a trapped-ion quantum computer
• Decoherence due to elastic Rayleigh scattering
• Two-qubit entangling gates within arbitrarily long chains of trapped ions
• Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions
• Scalable and Parallel Tweezer Gates for Quantum Computing with Long Ion Strings
• Theory of robust multi-qubit non-adiabatic gates for trapped-ions
• Use of global interactions in efficient quantum circuit constructions
• Comparing Zeeman qubits to hyperfine qubits in the context of the surface code: ${}^{174}$Yb${}^{+}$ and ${}^{171}$Yb${}^{+}$
• Leakage mitigation for quantum error correction using a mixed qubit scheme
• Efficient eigenvalue determination for arbitrary Pauli products based on generalized spin-spin interactions

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• 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