Adaptive surface code for quantum error correction in the presence of temporary or permanent defects

Abstract

Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may correspond to individual qubits or to clusters and could potentially disrupt the code sufficiently to generate logical errors. In this paper, we explore a novel adaptive approach for surface code quantum error correction on a defective lattice. We show that combining an appropriate defect detection algorithm and a quarantine of the identified zone allows one to preserve the advantage of quantum error correction at finite code sizes, at the cost of a qubit overhead that scales with the size of the defect. Our numerics indicate that the code's threshold need not be significantly affected; for example, for a certain scenario where small defects repeatedly arise in each logical qubit, the noise threshold is $2.7\%$ (versus the defect-free case of $2.9\%$). These results pave the way to the experimental implementation of large-scale quantum computers where defects will be inevitable.

arXiv comment12 pages, 9 figures

References in corpus (23)

• Surface codes: Towards practical large-scale quantum computation
• Quantum Error Correction for Quantum Memories
• Suppressing quantum errors by scaling a surface code logical qubit
• How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits
• Roads towards fault-tolerant universal quantum computation
• Exponential suppression of bit or phase flip errors with repetitive error correction
• Correlated Charge Noise and Relaxation Errors in Superconducting Qubits
• Universal fault-tolerant quantum computation with only transversal gates and error correction
• Resolving catastrophic error bursts from cosmic rays in large arrays of superconducting qubits
• Decoding Across the Quantum LDPC Code Landscape
• Assessing the progress of trapped-ion processors towards fault-tolerant quantum computation
• Thresholds for topological codes in the presence of loss
• Poking holes and cutting corners to achieve Clifford gates with the surface code
• Linear-Time Maximum Likelihood Decoding of Surface Codes over the Quantum Erasure Channel
• Code Deformation and Lattice Surgery Are Gauge Fixing
• Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead
• Fault-tolerance thresholds for the surface code with fabrication errors
• Quantum Error Correction of a Qubit Loss in an Addressable Atomic System
• Surface Code Error Correction on a Defective Lattice
• Handling Leakage with Subsystem Codes
• Q3DE: A fault-tolerant quantum computer architecture for multi-bit burst errors by cosmic rays
• LILLIPUT: A Lightweight Low-Latency Lookup-Table Based Decoder for Near-term Quantum Error Correction
• Hardware-Efficient, Fault-Tolerant Quantum Computation with Rydberg Atoms

Cited by in corpus (10)

• Fault-tolerant hyperbolic Floquet quantum error correcting codes
• Detrimental non-Markovian errors for surface code memory
• LUCI in the Surface Code with Dropouts
• Snakes and Ladders: Adapting the surface code to defects
• Accommodating Fabrication Defects on Floquet Codes with Minimal Hardware Requirements
• Synchronization for Fault-Tolerant Quantum Computers
• Fundamental thresholds for computational and erasure errors via the coherent information
• Averting multi-qubit burst errors in surface code magic state factories
• Minimising surface-code failures using a color-code decoder
• Routing-based technique for defect mitigation in quantum error correction