galois_color

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: |

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.'
 

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.

codes/quantum/qudits_galois/stabilizer/qldpc/galois_topological.yml → 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

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'