Concatenation Schemes for Topological Fault-tolerant Quantum Error Correction

• Published in: arXiv.org
• Main Authors: Li, Zhaoyi, Kim, Isaac, Hayden, Patrick
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 06.08.2023
• Subjects: Circuits; Clusters; Decoding; Dimensional tolerances; Error analysis; Error correction; Error detection; Fault tolerance; Physics - Quantum Physics
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2209.09390

We investigate a family of fault-tolerant quantum error correction schemes based on the concatenation of small error detection or error correction codes with the three-dimensional cluster state. We propose fault-tolerant state preparation and decoding schemes that effectively convert every circuit-level error into an erasure error, leveraging the cluster state's high threshold against such errors. We find a set of codes for which such a conversion is possible, and study their performance against the standard circuit-level depolarizing model. Our best performing scheme, which is based on a concatenation with a classical code, improves the threshold by \(16.5\%\) and decreases the spacetime overhead by \(32\%\) compared to the scheme without concatenation, with each scheme subject to a physical error rate of \(10^{-3}\) and achieving a logical error rate of \(10^{-6}\).