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[[144,12,12]] gross
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valbert4 committed Mar 28, 2024
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3 changes: 2 additions & 1 deletion codes/quantum/properties/stabilizer/qldpc/qldpc.yml
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Expand Up @@ -70,7 +70,8 @@ features:
decoders:
- 'Belief-propagation (BP) decoder \cite{arxiv:0801.1241} is a quantum version of the classical BP decoder, but performance suffers due to degeneracy \cite{arxiv:2012.15297}. Various post-processing algorithms have been proposed (see below and also Ref. \cite{doi:10.1109/MILCOM58377.2023.10356284}).'
- 'BP-OSD decoder, scaling as \(O(n^3)\), adds a post-processing step based on ordered statistics decoding (OSD) to the belief propogation (BP) decoder \cite{arxiv:1904.02703}.'
- 'BP-OSD decoder, scaling as \(O(n^3)\), adds a post-processing step based on ordered statistics decoding (OSD) to the belief propogation (BP) decoder \cite{arxiv:1904.02703}.
For an open-source implementation, see \cite{arxiv:2005.07016,manual:{Roffe, Joschka. "LDPC: Python tools for low density parity check codes." (2022).}}.'
- 'Neural BP decoder \cite{arxiv:2212.10245} for qubit codes.'
- 'Partially and fully decoupled BP decoders, which use the decoupling representation, yield improvements against depolarizing noise \cite{arxiv:2305.17505}.'
- 'Message-passing decoder utilizing stabilizer inactivation (MP-SI a.k.a. BP-SI) for CSS-type QLDPC qubit codes \cite{arxiv:2205.06125}.'
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32 changes: 32 additions & 0 deletions codes/quantum/qubits/stabilizer/qldpc/algebraic/gross.yml
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#######################################################
## This is a code entry in the error correction zoo. ##
## https://github.com/errorcorrectionzoo ##
#######################################################

code_id: gross
physical: qubits
logical: qubits

name: '\([[144,12,12]]\) gross code'
introduced: '\cite{arxiv:2308.07915}'

description: |
A BB QLDPC code which requires less physical and ancilla qubits (for syndrome extraction) than the surface code with the same number of logical qubits and distance.
The name stems from the fact that a gross is a dozen dozen.
# https://twitter.com/jaygambetta/status/1773099803561381995

features:
rate: 'An ancilla-added rate of \(1/24\).
In contrast, the distance-13 surface code has ancilla-added rate \(1/338\).'

relations:
parents:
- code_id: qcga


# Begin Entry Meta Information
_meta:
# Change log - most recent first
changelog:
- user_id: VictorVAlbert
date: '2024-03-28'
10 changes: 3 additions & 7 deletions codes/quantum/qubits/stabilizer/qldpc/algebraic/qcga.yml
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Expand Up @@ -8,12 +8,10 @@ physical: qubits
logical: qubits

# name: 'Bravyi-Cross-Gambetta-Maslov-Rall-Yoder (BCGMRY) code'
name: 'Bivariate bicycle code'
name: 'Bivariate bicycle (BB) code'
short_name: 'BB'
introduced: '\cite{arxiv:2308.07915}'

alternative_names:
- 'Gross (i.e., dozen) code'

description: |
One of several Abelian 2BGA codes which admit time-optimal syndrome measurement circuits that can be implemented in a two-layer
architecture, a generalization of the square-lattice architecture
Expand All @@ -24,9 +22,7 @@ description: |
features:
rate: 'When ancilla qubit overhead is included, the encoding rate surpasses that of the surface code.
A general \([[n,k,d]]\) bivariate bicycle code requires \(n\) ancilla qubits for encoding, meaning that its \textit{ancilla-added encoding rate} is \(k/2n\).
For example, the \([[144,12,12]]\) code has ancilla-added rate \(1/24\).
In contrast, the distance-13 surface code has ancilla-added rate \(1/338\).'
A general \([[n,k,d]]\) bivariate bicycle code requires \(n\) ancilla qubits for encoding, meaning that its \textit{ancilla-added encoding rate} is \(k/2n\).'

fault_tolerance:
- 'Fault-tolerant state initialization using lattice surgery techniques \cite{arxiv:2110.10794,arxiv:2308.08648} and an ancillary surface code \cite{arxiv:2308.07915}.'
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