Asymptotically Good Quantum and Locally Testable Classical LDPC Codes

Panteleev, Pavel; Kalachev, Gleb

doi:10.48550/arxiv.2111.03654

Cited by 26 publications

(64 citation statements)

References 38 publications

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“…Here, we compare our construction with two recent papers on similar topics [12] [13]. The common feature of these constructions is that all of them use the same kind of twodimensional graph.…”

Section: B Discussionmentioning

confidence: 99%

“…The square appears because the left action commutes with the right action. The existence of squares is essential for the Tanner code construction in [12] and [13].…”

Section: Definition 6 (Left-right Cayley Graph) the Left-right Bipartitementioning

confidence: 99%

“…In this section, we introduce the locally minimal distance [24] [25] [12], and show that locally minimal distance is a lower bound of locally testable distance. This means that if we can show locally minimal distance is linear then locally testable distance is linear which implies constant soundness.…”

Section: B Locally Minimalmentioning

confidence: 99%

“…Despite these progress, the existence of the ultimate c 3 -LTCs remains uncertain. Recently, two papers [12] [13] show the existence of c 3 -LTCs using Tanner codes. In this work, we show the existence of c 3 -LTCs using lossless expanders.…”

Section: Introductionmentioning

confidence: 99%

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$c^3$-Locally Testable Codes from Lossless Expanders

Lin¹,

Hsieh²

2022

Preprint

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A locally testable code (LTC) is an error correcting code with a property tester. The tester tests if a word is codeword by reading constant random bits and rejects the word with probability proportional to the distance from the word to the closest codeword. An important open question until recently is whether there exist c 3 -LTCs which are LTCs with constant rate, constant relative distance and constant locality. In this work, we construct a new LTC family using 1-sided lossless expanders and balanced products.

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Section: B Discussionmentioning

confidence: 99%

“…The square appears because the left action commutes with the right action. The existence of squares is essential for the Tanner code construction in [12] and [13].…”

Section: Definition 6 (Left-right Cayley Graph) the Left-right Bipartitementioning

confidence: 99%

Section: B Locally Minimalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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$c^3$-Locally Testable Codes from Lossless Expanders

Lin¹,

Hsieh²

2022

Preprint

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“…Update While the current paper was being prepared for publication, Panteleev and Kalachev [PK21a] found a breakthrough construction of explicit good quantum LDPC codes.…”

Section: Introductionmentioning

confidence: 99%

Explicit Abelian Lifts and Quantum LDPC Codes

Jeronimo¹,

Mittal²,

O’Donnell³

et al. 2021

Preprint

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Real-time decoding for fault-tolerant quantum computing: progress, challenges and outlook

Battistel¹,

Chamberland

Johar

et al. 2023

Nano Futures

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Quantum computing is poised to solve practically useful problems which are computationally intractable for classical supercomputers. However, the current generation of quantum computers are limited by errors that may only partially be mitigated by developing higher-quality qubits. Quantum error correction~(QEC) will thus be necessary to ensure fault tolerance. QEC protects the logical information by cyclically measuring syndrome information about the errors. An essential part of QEC is the decoder, which uses the syndrome to compute the likely effect of the errors on the logical degrees of freedom and provide a tentative correction. The decoder must be accurate, fast enough to keep pace with the QEC~cycle (e.g., on a microsecond timescale for superconducting qubits) and with hard real-time system integration to support logical operations. As such, real-time decoding is essential to realize fault-tolerant quantum computing and to achieve quantum advantage. In this work, we highlight some of the key challenges facing the implementation of real-time decoders while providing a succinct summary of the progress to-date. Furthermore, we lay out our perspective for the future development and provide a possible roadmap for the field of real-time decoding in the next few years. As the quantum hardware is anticipated to scale up, this perspective article will provide a guidance for researchers, focusing on the most pressing issues in real-time decoding and facilitating the development of solutions across quantum and computer science.

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Asymptotically Good Quantum and Locally Testable Classical LDPC Codes

Cited by 26 publications

References 38 publications

$c^3$-Locally Testable Codes from Lossless Expanders

$c^3$-Locally Testable Codes from Lossless Expanders

Explicit Abelian Lifts and Quantum LDPC Codes

Real-time decoding for fault-tolerant quantum computing: progress, challenges and outlook

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