From 096a35b03a284184a20391a9381ce7a0e070da55 Mon Sep 17 00:00:00 2001 From: Fe-r-oz Date: Wed, 18 Sep 2024 20:56:28 +0500 Subject: [PATCH] add references for product codes --- docs/make.jl | 2 +- docs/src/Quantum/product_codes.md | 21 +++------ docs/src/Quantum/quantum_code.md | 2 +- docs/src/{refs.bib => references.bib} | 62 +++++++++++++++++++++++++++ 4 files changed, 70 insertions(+), 17 deletions(-) rename docs/src/{refs.bib => references.bib} (61%) diff --git a/docs/make.jl b/docs/make.jl index 344f2484..6784b644 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -1,6 +1,6 @@ using DocumenterCitations, Documenter, CodingTheory -bib = CitationBibliography(joinpath(@__DIR__, "src", "refs.bib"); style = :numeric) +bib = CitationBibliography(joinpath(@__DIR__, "src", "references.bib"); style = :numeric) Documenter.makedocs(; plugins=[bib], diff --git a/docs/src/Quantum/product_codes.md b/docs/src/Quantum/product_codes.md index c555d28d..d7447bed 100644 --- a/docs/src/Quantum/product_codes.md +++ b/docs/src/Quantum/product_codes.md @@ -1,20 +1,11 @@ # Product Codes -# Notes -* The hypergraph product is defined in "J. Tillich, G. Zémor. Quantum LDPC codes - with positive rate and minimum distance proportional to n^(1/2). (2013) - arXiv:0903.0566v2" -* The generalized Shor code is defined in "D. Bacon and A. Casaccino. Quantum - error correcting subsystem codes from two classical linear codes. (2006) - http://arxiv.org/abs/quant-ph/0610088" -* Hyperbicycle codes are found in "Quantum ``hyperbicycle'' low-density parity check - codes with finite rate" and "Quantum Kronecker sum-product low-density parity-check - codes with finite rate". -* Generealized bicycle codes are are found in "Quantum ``hyperbicycle'' low-density parity check - codes with finite rate", "Quantum kronecker sum-product low-density parity- check codes with - finite rate", and "Degenerate Quantum LDPC Codes With Good Finite Length Performance". -* The generalized hypergraph product is defined in "Degenerate Quantum LDPC Codes With Good Finite Length Performance". -* The bias-tailored lifted product is defined in "Bias-tailored quantum LDPC codes". +- Hypergraph product: [tillich2009quantum](@cite) +- Generalized Shor: [bacon2006quantum](@cite) +- Hyperbicycle: [pryadko2013quantum](@cite) +- Generealized bicycle: [pryadko2013quantum](@cite), [kovalev2013quantum](@cite), [kovalev1212quantum](@cite), [panteleev2021degenerate](@cite) +- Generalized hypergraph product: [panteleev2021degenerate](@cite) +- Bias-tailored lifted product: [roffe2023bias](@cite) ```@autodocs diff --git a/docs/src/Quantum/quantum_code.md b/docs/src/Quantum/quantum_code.md index 3c45f06d..9f3b77ce 100644 --- a/docs/src/Quantum/quantum_code.md +++ b/docs/src/Quantum/quantum_code.md @@ -1,5 +1,5 @@ * `char_vec`: a length `2n` vector with elements in the `Z/(2p)` if - `chracteristic(field(C1))` is 2 and `Z/(p)` otherwise. The first `n` elements + `characteristic(field(C1))` is 2 and `Z/(p)` otherwise. The first `n` elements specify the exponents of the `X` phases and second `n` the exponents of the `Z` phases; a missing argument will be set to the all-zero vector diff --git a/docs/src/refs.bib b/docs/src/references.bib similarity index 61% rename from docs/src/refs.bib rename to docs/src/references.bib index a1fe8c59..a06832bc 100644 --- a/docs/src/refs.bib +++ b/docs/src/references.bib @@ -111,3 +111,65 @@ @misc{Vasmer_2020 author={Vasmer, Michael}, year={2020} } + +% Product Codes + +@article{bacon2006quantum, + title={Quantum error correcting subsystem codes from two classical linear codes}, + author={Bacon, Dave and Casaccino, Andrea}, + journal={arXiv preprint quant-ph/0610088}, + year={2006} +} + +@inproceedings{tillich2009quantum, + title={Quantum LDPC codes with positive rate and minimum distance proportional to n $1/2$}, + author={Tillich, J-P and Zemor, G}, + booktitle={2009 IEEE International Symposium on Information Theory} +} + +@inproceedings{pryadko2013quantum, + title={Quantum``hyperbicycle''low-stabilizer-weight finite-rate error correction codes}, + author={Pryadko, Leonid P and Kovalev, Alexey A}, + booktitle={APS March Meeting Abstracts}, + volume={2013}, + pages={M27--008}, + year={2013} +} + +@article{kovalev2013quantum, + title={Quantum Kronecker sum-product low-density parity-check codes with finite rate}, + author={Kovalev, Alexey A and Pryadko, Leonid P}, + journal={Physical Review A—Atomic, Molecular, and Optical Physics}, + volume={88}, + number={1}, + pages={012311}, + year={2013}, + publisher={APS} +} + +@article{kovalev1212quantum, + title={Quantum “hyperbicycle” low density parity check codes with finite rate}, + author={Kovalev, AA and Pryadko, LP}, + journal={arXiv}, + volume={1212} +} + +@article{panteleev2021degenerate, + title={Degenerate quantum LDPC codes with good finite length performance}, + author={Panteleev, Pavel and Kalachev, Gleb}, + journal={Quantum}, + volume={5}, + pages={585}, + year={2021}, + publisher={Verein zur F{\"o}rderung des Open Access Publizierens in den Quantenwissenschaften} +} + +@article{roffe2023bias, + title={Bias-tailored quantum LDPC codes}, + author={Roffe, Joschka and Cohen, Lawrence Z and Quintavalle, Armanda O and Chandra, Daryus and Campbell, Earl T}, + journal={Quantum}, + volume={7}, + pages={1005}, + year={2023}, + publisher={Verein zur F{\"o}rderung des Open Access Publizierens in den Quantenwissenschaften} +}