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.

12 pages, 9 figures

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• Q3DE: A fault-tolerant quantum computer architecture for multi-bit burst errors by cosmic rays
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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