1Department of Physics, Stanford University, Stanford, CA 94305, USA
2Department of Computer Science, University of California, Davis, CA 95616, USA
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Abstract
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 $10^{-6}$.
Featured image: An illustration depicting the cellular structure of the concatenated [[2, 1, 1]] lattice, an augmented 3D cluster state employed to enhance fault-tolerance in our study.
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Cited by
[1] Thomas J. Bell, Love A. Pettersson, and Stefano Paesani, “Optimizing Graph Codes for Measurement-Based Loss Tolerance”, PRX Quantum 4 2, 020328 (2023).
[2] Dimiter Ostrev, Davide Orsucci, Francisco Lázaro, and Balazs Matuz, “Classical product code constructions for quantum Calderbank-Shor-Steane codes”, arXiv:2209.13474, (2022).
The above citations are from SAO/NASA ADS (last updated successfully 2023-08-26 14:28:31). The list may be incomplete as not all publishers provide suitable and complete citation data.
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This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
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