Leakage mitigation for quantum error correction using a mixed qubit scheme

Abstract

Leakage errors take qubits out of the computational subspace and will accumulate if not addressed. A leaked qubit will reduce the effectiveness of quantum error correction protocols due to the cost of implementing leakage reduction circuits and the harm caused by interacting leaked states with qubit states. Ion trap qubits driven by Raman gates have a natural choice between qubits encoded in magnetically insensitive hyperfine states that can leak and qubits encoded in magnetically sensitive Zeeman states of the electron spin that cannot leak. In our previous work, we compared these two qubits in the context of the toric code with a depolarizing leakage error model and found that for magnetic field noise with a standard deviation less than 32 $\mu$G that the ${}^{174}$Yb${}^{+}$ Zeeman qubit outperforms the ${}^{171}$Yb${}^{+}$ hyperfine qubit. Here we examine a physically motivated leakage error model based on ions interacting via the Molmer-Sorenson gate. We find that this greatly improves the performance of hyperfine qubits but the Zeeman qubits are more effective for magnetic field noise with a standard deviation less than 10 $\mu$G. At these low magnetic fields, we find that the best choice is a mixed qubit scheme where the hyperfine qubits are the ancilla and the leakage is handled without the need of an additional leakage reduction circuit.

arXiv comment8 pages, 6 figures, comments welcome

References in corpus (50)

• Topological quantum memory
• Quantum computing with trapped ions
• Quantum computation with ions in thermal motion
• Fault-tolerant quantum computation with high threshold in two dimensions
• Demonstration of a small programmable quantum computer with atomic qubits
• High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions
• High-fidelity quantum logic gates using trapped-ion hyperfine qubits
• Manipulation and Detection of a Trapped Yb+ Ion Hyperfine Qubit
• Microwave quantum logic gates for trapped ions
• Single-qubit quantum memory exceeding $10$-minute coherence time
• Low-distance Surface Codes under Realistic Quantum Noise
• Blueprint for a microwave trapped-ion quantum computer
• Topological quantum computing with a very noisy network and local error rates approaching one percent
• Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code
• Single-qubit-gate error below 10^-4 in a trapped ion
• Ultrahigh Error Threshold for Surface Codes with Biased Noise
• Sympathetic cooling of ${}^{9}B{e}^{+}$ and ${}^{24}M{g}^{+}$ for quantum logic
• Quantum information processing with trapped ions
• Errors in trapped-ion quantum gates due to spontaneous photon scattering
• Fault-tolerant quantum error detection
• Multi-Element Logic Gates for Trapped-Ion Qubits
• Fault tolerant quantum computation with very high threshold for loss errors
• Isotope-selective photo-ionization for calcium ion trapping
• High-fidelity trapped-ion quantum logic using near-field microwaves
• Robust two-qubit gates in a linear ion crystal using a frequency-modulated driving force
• Repeated multi-qubit readout and feedback with a mixed-species trapped-ion register
• Basic circuit compilation techniques for an ion-trap quantum machine
• A long-lived Zeeman trapped-ion qubit
• Hyperfine Coherence in the Presence of Spontaneous Photon Scattering
• Operation and intrinsic error budget of a two-qubit cross-resonance gate
• High Speed, High Fidelity Detection of an Atomic Hyperfine Qubit
• Multi-Species Trapped Ion Node for Quantum Networking
• Hybrid quantum logic and a test of Bell's inequality using two different atomic isotopes
• Decoherence due to elastic Rayleigh scattering
• Coping with qubit leakage in topological codes
• Decoherence of a single-ion qubit immersed in a spin-polarized atomic bath
• Simulating the performance of a distance-3 surface code in a linear ion trap
• Understanding the effects of leakage in superconducting quantum error detection circuits
• Entanglement-based dc magnetometry with separated ions
• Coherent Manipulation of a Ca Spin Qubit in a Micro Ion Trap
• A leakage-resilient approach to fault-tolerant quantum computing with superconducting elements
• Spectroscopy of a synthetic trapped ion qubit
• Tutorial: The trapped-ion qubit toolbox
• High-fidelity state detection and tomography of a single ion Zeeman qubit
• Error- and Loss-Tolerances of Surface Codes with General Lattice Structures
• Comparing Zeeman qubits to hyperfine qubits in the context of the surface code: ${}^{174}$Yb${}^{+}$ and ${}^{171}$Yb${}^{+}$
• Transport Implementation of the Bernstein-Vazirani Algorithm with Ion Qubits
• Handling Leakage with Subsystem Codes
• Practical Topological Cluster State Quantum Computing Requires Loss Below 1%
• Fault-Tolerant Quantum Computation for Singlet-Triplet Qubits with Leakage Errors

Cited by in corpus (24)

• Overcoming leakage in scalable quantum error correction
• Quantum Error Correction with Metastable States of Trapped Ions Using Erasure Conversion
• Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics
• Deterministic correction of qubit loss
• Leakage detection for a transmon-based surface code
• Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions
• A hardware-efficient leakage-reduction scheme for quantum error correction with superconducting transmon qubits
• Real-time calibration with spectator qubits
• Randomized benchmarking for non-Markovian noise
• Efficient and robust certification of genuine multipartite entanglement in noisy quantum error correction circuits
• Comparing Two-Qubit and Multi-Qubit Gates within the Toric Code
• SPAM-Robust Multi-axis Quantum Noise Spectroscopy in Temporally Correlated Environments
• ERASER: Towards Adaptive Leakage Suppression for Fault-Tolerant Quantum Computing
• Local Clustering Decoder as a fast and adaptive hardware decoder for the surface code
• Surface Code with Imperfect Erasure Checks
• Error metric for non-trace-preserving quantum operations
• Taming Rydberg Decay with Measurement-based Quantum Computation
• Locating Rydberg Decay Error in SWAP-Leakage Reduction Circuit Protocol
• Accurate Leakage Speculation for Quantum Error Correction
• Leakage Mobility in Superconducting Qubits as a Leakage Reduction Unit
• Cross-platform certification of the qubit space with a minimal number of parameters
• Passive leakage removal unit based on a disordered transmon array
• Incoherent Approximation of Leakage in Quantum Error Correction
• Feedforward suppression of readout-induced faults in quantum error correction