holographic_steane

codes/quantum/qubits/small_distance/small/stab_5_1_3.yml

@@ -79,7 +79,7 @@ relations:
       See Ref. \cite{arxiv:2211.03094} for the first few codes in a different extension of the five-qubit perfect code.'
     - code_id: happy
       detail: 'The five-qubit code is the smallest (i.e., radius-one) single-qubit HaPPY code.
-      The five-qubit encoding isometry tiles various holographic codes because its corresponding tensor is perfect \cite{arxiv:1503.06237}.'
+      The five-qubit encoding isometry tiles various holographic codes because its corresponding encoding isometry tensor is a \hyperref[topic:ame]{perfect tensor} \cite{arxiv:1503.06237}.'
     - code_id: quantum_perfect
       detail: 'The five-qubit code is the smallest perfect code and is a member of the perfect qubit code family \([[(4^r-1)/3, (4^r-1)/3 - 2r, 3]]\) for \(r = 2\).'
     - code_id: stabilizer_over_gf4

codes/quantum/qubits/small_distance/small/steane/steane.yml

@@ -104,6 +104,12 @@ relations:
       detail: 'The Steane code is a group-representation code with \(G\) being the \(2O\) subgroup of \(SU(2)\) \cite{arxiv:2306.11621}.'
     - code_id: concatenated_steane
       detail: 'The concatenated Steane code at level \(m=1\) is the Steane code.'
+    - code_id: holographic_steane
+      detail: 'The Steane code is the smallest heptagon holographic code.
+      The encoding of more general heptagon holographic codes is a holographic tensor network consisting of encoding isometries for the Steane code, which are block-perfect tensors.'
+    - code_id: block_perfect
+      detail: 'The Steane code is the smallest heptagon holographic code.
+      The encoding of more general heptagon holographic codes is a holographic tensor network consisting of encoding isometries for the Steane code, which are block-perfect tensors.'
   cousins:
     - code_id: quantum_cyclic
       detail: 'The Steane code is equivalent to a cyclic code via qubit permutations \cite[Exam. 1]{arxiv:1108.5490}.'

codes/quantum/qubits/stabilizer/happy.yml → codes/quantum/qubits/stabilizer/holographic/happy.yml

@@ -12,7 +12,6 @@ short_name: 'HaPPY'
 introduced: '\cite{arxiv:1503.06237}'
 
 description: |
-  Also known as a \textit{hyperbolic pentagon code (HyPeC)}.
   Holographic code constructed out of a network of hexagonal \hyperref[topic:ame]{perfect tensors} that tesselates hyperbolic space.
   Physical qubits are associated with uncontracted tensor legs at the boundary of the tesselation, while logical qubits are associated with uncontracted legs in the bulk.
   The code serves as a minimal model for several aspects of the AdS/CFT holographic duality \cite{arxiv:1706.08823} and potentially a dF/CFT duality \cite{arxiv:2201.11658}.
@@ -26,7 +25,7 @@ description: |
 
   The \textit{single-qubit HaPPY code} has a central pentagon encoding one bulk operator and hexagons tiling all other layers.
   The \textit{pentagon-hexagon HaPPY code} has alternating layers of pentagons and hexagons in the tiling.
-  The \textit{pentagon HaPPY code} consists of a purely pentagonal tiling.
+  The \textit{pentagon HaPPY code} (a.k.a. the hyperbolic pentagon code, or HyPeC) consists of a purely pentagonal tiling.
 
 #The bulk legs correspond to indices for logical input, while the boundary legs can be interpreted as the physical encoding.
 #In the Heisenberg picture, the code can be thought of as encoding operators in the bulk of Anti de Sitter (AdS) space (formed by logical qudits) into operators on the boundary of the corresponding Conformal Field Theory (CFT, formed by the physical qudits).
@@ -69,6 +68,8 @@ relations:
   cousins:
     - code_id: majorana_stab
       detail: 'HaPPY code Hamiltonian can be expressed in terms of mutually commuting weight-two (two-body) Majorana operators \cite{arxiv:1905.03268}.'
+    - code_id: ame
+      detail: 'The encoding of a HaPPy code is a holographic tensor network consisting of pentagon and hexagon \hyperref[topic:ame]{perfect tensors}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/stabilizer/holographic/holographic_steane.yml

@@ -0,0 +1,46 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: holographic_steane
+physical: qubits
+logical: qubits
+
+name: 'Heptagon holographic code'
+introduced: '\cite{arxiv:1806.06472}'
+
+alternative_names:
+  - 'Holographic Steane code'
+
+description: |
+  Holographic tensor-network code constructed out of a network of encoding isometries of the Steane code.
+
+features:
+  decoders:
+    - 'Optimal erasure decoder \cite{arxiv:1806.06472}.'
+
+  threshold:
+    - '\(~33\%\) under erasure noise using optimal erasure decoder \cite{arxiv:1806.06472}.'
+    - '\(9.4\%\) under depolarizing noise using tensor-network decoder \cite{arxiv:2012.07317}.'
+
+
+relations:
+  parents:
+    - code_id: holographic_tensor
+      detail: 'The encoding of the heptagon holographic code is a holographic tensor network consisting of encoding isometries for the Steane code, which are block-perfect tensors.'
+  cousins:
+    - code_id: block_perfect
+      detail: 'The encoding of the heptagon holographic code is a holographic tensor network consisting of encoding isometries for the Steane code, which are block-perfect tensors.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2022-07-28'
+    - user_id: VictorVAlbert
+      date: '2021-12-29'
+    - user_id: JoelRajakumar
+      date: '2021-12-20'