diff --git a/codes/quantum/qubits/stabilizer/topological/color/2d_color/2d_color.yml b/codes/quantum/qubits/stabilizer/topological/color/2d_color/2d_color.yml index 3e86df675..cfd57a286 100644 --- a/codes/quantum/qubits/stabilizer/topological/color/2d_color/2d_color.yml +++ b/codes/quantum/qubits/stabilizer/topological/color/2d_color/2d_color.yml @@ -75,7 +75,7 @@ relations: See Ref. \cite{arxiv:2112.13617} for an alternative non-CSS extension of 2D color codes.' - code_id: qudit_color detail: 'Modular-qudit 2D color codes reduce to 2D color codes for \(q=2\).' - - code_id: galois_topological + - code_id: galois_color detail: 'Galois-qudit 2D color codes reduce to 2D color codes for \(q=2\).' - code_id: quantum_double_abelian detail: | diff --git a/codes/quantum/qudits/stabilizer/topological/quantum_double_abelian.yml b/codes/quantum/qudits/stabilizer/topological/quantum_double_abelian.yml index e77db348c..b39a6c7e0 100644 --- a/codes/quantum/qudits/stabilizer/topological/quantum_double_abelian.yml +++ b/codes/quantum/qudits/stabilizer/topological/quantum_double_abelian.yml @@ -32,9 +32,7 @@ features: relations: parents: - code_id: tqd_abelian - detail: 'The anyon theory corresponding to Abelian quantum double codes is defined by an Abelian group and trivial cocycle. - All Abelian TQD codes can be realized as modular-qudit stabilizer codes by starting with an Abelian quantum double model along with a family of Abelian TQDs that generalize the double semion anyon theory and \hyperref[topic:code-switching]{condensing} certain bosonic anyons \cite{arxiv:2211.03798}. - Upon gauging some symmetries \cite{arxiv:1202.3120,arxiv:1605.01640,arxiv:1806.08679,arxiv:1806.08679}, Type-I and II \(\mathbb{Z}_2^3\) TQDs realize the same topological order as certain Abelian quantum double models \cite{arxiv:hep-th/9511195,arxiv:1508.03468,arxiv:2112.12757}.' + detail: 'The anyon theory corresponding to Abelian quantum double codes is defined by an Abelian group and trivial cocycle. All Abelian TQD codes can be realized as modular-qudit stabilizer codes by starting with an Abelian quantum double model along with a family of Abelian TQDs that generalize the double semion anyon theory and \hyperref[topic:code-switching]{condensing} certain bosonic anyons \cite{arxiv:2211.03798}. Upon gauging some symmetries \cite{arxiv:1202.3120,arxiv:1605.01640,arxiv:1806.08679,arxiv:1806.08679}, Type-I and II \(\mathbb{Z}_2^3\) TQDs realize the same topological order as certain Abelian quantum double models \cite{arxiv:hep-th/9511195,arxiv:1508.03468,arxiv:2112.12757}.' - code_id: quantum_double detail: 'The anyon theory corresponding to (Abelian) quantum double codes is defined by an (Abelian) group.' diff --git a/codes/quantum/qudits/stabilizer/topological/qudit_color.yml b/codes/quantum/qudits/stabilizer/topological/qudit_color.yml index 96089fdcc..5810f6f3e 100644 --- a/codes/quantum/qudits/stabilizer/topological/qudit_color.yml +++ b/codes/quantum/qudits/stabilizer/topological/qudit_color.yml @@ -12,7 +12,7 @@ introduced: '\cite{arxiv:1503.08800}' # assumed to be lattice code, diff from code_id:color, as motivated by paper description: | - An extension of color codes on lattices to modular qudits. + Extension of the color code to lattices of modular qudits. Codes are defined analogous to qubit color codes on suitable lattices of any spatial dimension, but a directionality is required in order to make the modular-qudit stabilizer commute. This can be done by puncturing a hyperspherical lattice \cite{arxiv:1311.0879} or constructing a star-bipartition; see \cite[Sec. III]{arxiv:1503.08800}. Logical dimension is determined by the genus of the underlying surface (for closed surfaces), types of boundaries (for open surfaces), and/or any twist defects present. diff --git a/codes/quantum/qudits_galois/stabilizer/qldpc/galois_topological.yml b/codes/quantum/qudits_galois/stabilizer/topological/galois_color.yml similarity index 50% rename from codes/quantum/qudits_galois/stabilizer/qldpc/galois_topological.yml rename to codes/quantum/qudits_galois/stabilizer/topological/galois_color.yml index 09373c692..f81b2b90e 100644 --- a/codes/quantum/qudits_galois/stabilizer/qldpc/galois_topological.yml +++ b/codes/quantum/qudits_galois/stabilizer/topological/galois_color.yml @@ -3,27 +3,29 @@ ## https://github.com/errorcorrectionzoo ## ####################################################### -code_id: galois_topological +code_id: galois_color physical: galois logical: galois -name: 'Galois-qudit topological code' -introduced: '\cite{arxiv:quant-ph/0609070,doi:10.1109/CIG.2010.5592860,arxiv:1202.3338}' +name: 'Galois-qudit color code' +introduced: '\cite{doi:10.1109/CIG.2010.5592860}' alternative_names: - - '\(\mathbb{F}_q\)-qudit topological code' + - '\(\mathbb{F}_q\)-qudit color code' description: | - Abelian topological code, such as a 2D surface \cite{arxiv:quant-ph/0609070,arxiv:1202.3338} or 2D color \cite{doi:10.1109/CIG.2010.5592860} code, constructed on lattices of Galois qudits. + Extension of the color code to 2D lattices of Galois qudits. relations: parents: - code_id: galois_css - code_id: 2d_stabilizer - - code_id: topological_abelian + - code_id: generalized_homological_product_css + - code_id: quantum_double + detail: 'A Galois qudit for \(q=p^m\) can be decomposed into a Kronecker product of \(m\) modular qudits \cite{doi:10.1109/18.959288}\cite[Sec. 5.3]{arxiv:quant-ph/0501074}\cite{preset:GottesmanBook}. Galois-qudit color codes yield Abelian quantum-double codes with Abelian-group topological order via this decomposition.' cousins: - code_id: quantum_double_abelian - detail: 'A Galois qudit for \(q=p^m\) can be decomposed into a Kronecker product of \(m\) modular qudits \cite{doi:10.1109/18.959288}\cite[Sec. 5.3]{arxiv:quant-ph/0501074}\cite{preset:GottesmanBook}. Galois-qudit topological surface and color codes yield Abelian quantum-double codes via this decomposition.' + detail: 'A Galois qudit for \(q=p^m\) can be decomposed into a Kronecker product of \(m\) modular qudits \cite{doi:10.1109/18.959288}\cite[Sec. 5.3]{arxiv:quant-ph/0501074}\cite{preset:GottesmanBook}. Galois-qudit color codes yield Abelian quantum-double codes with Abelian-group topological order via this decomposition.' # Begin Entry Meta Information diff --git a/codes/quantum/qudits_galois/stabilizer/topological/galois_topological.yml b/codes/quantum/qudits_galois/stabilizer/topological/galois_topological.yml new file mode 100644 index 000000000..8cfb448f6 --- /dev/null +++ b/codes/quantum/qudits_galois/stabilizer/topological/galois_topological.yml @@ -0,0 +1,36 @@ +####################################################### +## This is a code entry in the error correction zoo. ## +## https://github.com/errorcorrectionzoo ## +####################################################### + +code_id: galois_topological +physical: galois +logical: galois + +name: 'Galois-qudit surface code' +introduced: '\cite{arxiv:quant-ph/0609070,arxiv:1202.3338}' + +alternative_names: + - '\(\mathbb{F}_q\)-qudit surface code' + +description: | + Extension of the surface code to 2D lattices of Galois qudits. + +relations: + parents: + - code_id: galois_css + - code_id: 2d_stabilizer + - code_id: generalized_homological_product_css + - code_id: quantum_double + detail: 'A Galois qudit for \(q=p^m\) can be decomposed into a Kronecker product of \(m\) modular qudits \cite{doi:10.1109/18.959288}\cite[Sec. 5.3]{arxiv:quant-ph/0501074}\cite{preset:GottesmanBook}. Galois-qudit surface codes yield Abelian quantum-double codes with \(GF(p^m)\cong \mathbb{Z}_p^m\) topological order via this decomposition.' + cousins: + - code_id: quantum_double_abelian + detail: 'A Galois qudit for \(q=p^m\) can be decomposed into a Kronecker product of \(m\) modular qudits \cite{doi:10.1109/18.959288}\cite[Sec. 5.3]{arxiv:quant-ph/0501074}\cite{preset:GottesmanBook}. Galois-qudit surface codes yield Abelian quantum-double codes with \(GF(p^m)\cong \mathbb{Z}_p^m\) topological order via this decomposition.' + + +# Begin Entry Meta Information +_meta: + # Change log - most recent first + changelog: + - user_id: VictorVAlbert + date: '2022-07-27'