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Good Quantum LDPC Codes with Linear Time Decoders

Dinur, Irit and Hsieh, Min-Hsiu and Lin, Ting-Chun and Vidick, Thomas (2022) Good Quantum LDPC Codes with Linear Time Decoders. . (Unpublished)

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We construct a new explicit family of good quantum low-density parity-check codes which additionally have linear time decoders. Our codes are based on a three-term chain (F₂(m×m))ⱽ −→^(δ0) (F₂ᵐ)ᴱ −→^(δ¹) F₂^F where V (X-checks) are the vertices, E (qubits) are the edges, and F (Z-checks) are the squares of a left-right Cayley complex, and where the maps are defined based on a pair of constant-size random codes C_A,C_B : F₂ᵐ → F₂^Δ where Δ is the regularity of the underlying Cayley graphs. One of the main ingredients in the analysis is a proof of an essentially-optimal robustness property for the tensor product of two random codes.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Hsieh, Min-Hsiu0000-0002-3396-8427
Vidick, Thomas0000-0002-6405-365X
Additional Information:Attribution 4.0 International (CC BY 4.0).
Record Number:CaltechAUTHORS:20221221-004759070
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:118566
Deposited By: George Porter
Deposited On:21 Dec 2022 20:31
Last Modified:21 Dec 2022 20:31

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