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Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits

Chamberland, Christopher and Noh, Kyungjoo (2020) Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits. npj Quantum Information, 6 . Art. No. 91. ISSN 2056-6387. https://resolver.caltech.edu/CaltechAUTHORS:20201130-140223226

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Abstract

Fault-tolerant quantum computing promises significant computational speedup over classical computing for a variety of important problems. One of the biggest challenges for realizing fault-tolerant quantum computing is preparing magic states with sufficiently low error rates. Magic state distillation is one of the most efficient schemes for preparing high-quality magic states. However, since magic state distillation circuits are not fault-tolerant, all the operations in the distillation circuits must be encoded in a large distance error-correcting code, resulting in a significant resource overhead. Here, we propose a fault-tolerant scheme for directly preparing high-quality magic states, which makes magic state distillation unnecessary. In particular, we introduce a concept that we call redundant ancilla encoding. The latter combined with flag qubits allows for circuits to both measure stabilizer generators of some code, while also being able to measure global operators to fault-tolerantly prepare magic states, all using nearest neighbor interactions. We apply such schemes to a planar architecture of the triangular color code family and demonstrate that our scheme requires at least an order of magnitude fewer qubits and space–time overhead compared to the most competitive magic state distillation schemes. Since our scheme requires only nearest-neighbor interactions in a planar architecture, it is suitable for various quantum computing platforms currently under development.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1038/s41534-020-00319-5DOIArticle
https://github.com/einsteinchris/MagicStatePrep.gitRelated ItemCode
ORCID:
AuthorORCID
Chamberland, Christopher0000-0003-3239-5783
Noh, Kyungjoo0000-0002-6318-8472
Additional Information:© The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Received 30 April 2020; Accepted 10 September 2020; Published 27 October 2020. C.C. acknowledges Yihe Tang and Milan Cvitkovic for their help in setting up the computing resources with the AWS clusters that were used for performing all the numerical simulations in this work. We would like to thank Earl Campbell, Aleksander Kubica and Fernando Brandao for useful discussions. We thank Simone Severini, Bill Vass and Dominique L’Eplattenier for their guidance and help with submitting the paper. We also thank Kevin Dothager for his help with IP. Data availability: All the data used to generate the results of our work can be found in the public repository https://github.com/einsteinchris/MagicStatePrep.git under the file name DataMagicStatePrepSim.nb. Code availability: The code used to generate the data in this work cannot be shared due to proprietary reasons. Author Contributions: C.C. and K.N. conceived the idea of redundant ancilla encoding, designed the fault-tolerant circuits for both syndrome extraction and measuring Hadamard, and proved the fault-tolerant properties of the magic state preparation protocol. C.C. performed the numerics and overhead analysis. C.C. and K.N. wrote the manuscript. The authors declare no competing interests.
Group:Institute for Quantum Information and Matter
Subject Keywords:Information theory and computation; Quantum information
Record Number:CaltechAUTHORS:20201130-140223226
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20201130-140223226
Official Citation:Chamberland, C., Noh, K. Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits. npj Quantum Inf 6, 91 (2020). https://doi.org/10.1038/s41534-020-00319-5
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106847
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:02 Dec 2020 20:28
Last Modified:02 Dec 2020 20:28

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