Decoding Schemes for Foliated Sparse Quantum Error Correcting Codes

Abstract

Foliated quantum codes are a resource for fault-tolerant measurement-based quantum error correction for quantum repeaters and for quantum computation. They represent a general approach to integrating a range of possible quantum error correcting codes into larger fault-tolerant networks. Here we present an efficient heuristic decoding scheme for foliated quantum codes, based on message passing between primal and dual code 'sheets'. We test this decoder on two different families of sparse quantum error correcting code: turbo codes and bicycle codes, and show reasonably high numerical performance thresholds. We also present a construction schedule for building such code states.

arXiv comment23 pages, 15 figures, accepted for publication in Phys. Rev. A

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Cited by in corpus (8)

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• Generating Fault-Tolerant Cluster States from Crystal Structures
• Decoding Holographic Codes with an Integer Optimisation Decoder
• Universal resource-efficient topological measurement-based quantum computation via color-code-based cluster states
• Single-shot and measurement-based quantum error correction via fault complexes
• Single-shot preparation of hypergraph product codes via dimension jump