Decoding holographic codes with an integer optimization decoder

Robert J. Harris; Elliot Coupe; Nathan McMahon; Gavin Brennen; Thomas M. Stace

doi:10.1103/PhysRevA.102.062417

Decoding holographic codes with an integer optimization decoder

Robert J. Harris, Elliot Coupe, Nathan McMahon, Gavin Brennen, Thomas M. Stace

ARC Centre of Excellence for Engineered Quantum Systems (EQuS)

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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Abstract

We develop a most likely error Pauli error decoding algorithm for stabilizer codes based on general purpose integer optimization. Using this decoder we analyze the performance of holographic codes against Pauli errors and find numerical evidence for thresholds against Pauli errors for bulk qubits. We compare the performance of holographic code families of various code rates and find phenomenological Pauli error thresholds ranging from 7% to 16%, depending on the code rate. Additionally we give numerical evidence that specific distance measures of the codes we consider scale polynomially with number of physical qubits.

Original language	English
Article number	062417
Pages (from-to)	062417-1-062417-6
Number of pages	6
Journal	Physical Review A: covering atomic, molecular, and optical physics and quantum information
Volume	102
Issue number	6
DOIs	https://doi.org/10.1103/PhysRevA.102.062417
Publication status	Published - 21 Dec 2020

Bibliographical note

Copyright 2020 American Physical Society. Firstly published in Physical Review A, 102(6), 062417. The original publication is available at https://doi.org/10.1103/PhysRevA.102.062417. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

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10.1103/PhysRevA.102.062417

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Cite this

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abstract = "We develop a most likely error Pauli error decoding algorithm for stabilizer codes based on general purpose integer optimization. Using this decoder we analyze the performance of holographic codes against Pauli errors and find numerical evidence for thresholds against Pauli errors for bulk qubits. We compare the performance of holographic code families of various code rates and find phenomenological Pauli error thresholds ranging from 7% to 16%, depending on the code rate. Additionally we give numerical evidence that specific distance measures of the codes we consider scale polynomially with number of physical qubits.",

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Decoding holographic codes with an integer optimization decoder. / Harris, Robert J.; Coupe, Elliot; McMahon, Nathan; Brennen, Gavin; Stace, Thomas M.

In: Physical Review A: covering atomic, molecular, and optical physics and quantum information, Vol. 102, No. 6, 062417, 21.12.2020, p. 062417-1-062417-6.

Research output: Contribution to journal › Article › peer-review

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T1 - Decoding holographic codes with an integer optimization decoder

AU - Harris, Robert J.

AU - Coupe, Elliot

AU - McMahon, Nathan

AU - Brennen, Gavin

AU - Stace, Thomas M.

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PY - 2020/12/21

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AB - We develop a most likely error Pauli error decoding algorithm for stabilizer codes based on general purpose integer optimization. Using this decoder we analyze the performance of holographic codes against Pauli errors and find numerical evidence for thresholds against Pauli errors for bulk qubits. We compare the performance of holographic code families of various code rates and find phenomenological Pauli error thresholds ranging from 7% to 16%, depending on the code rate. Additionally we give numerical evidence that specific distance measures of the codes we consider scale polynomially with number of physical qubits.

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Decoding holographic codes with an integer optimization decoder

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