holographic_6_1_3 + holographic_subsystem

codes/quantum/properties/block/tensor_network/holographic_tensor.yml

@@ -6,10 +6,12 @@
 code_id: holographic_tensor
 
 name: 'Holographic tensor-network code'
+introduced: '\cite{arxiv:2009.10329,arxiv:2109.11996}'
 
 description: |
   Quantum Lego code whose encoding isometry forms a holographic tensor network, i.e., a tensor network  tiling hyperbolic space.
-  The number of layers emanating form the central point of the tiling is the radius of the code.
+  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 number of layers emanating form the central point of the tiling is the \textit{radius} of the code.
 
   The encoding map often models radial time evolution for a fixed time slice in Anti de Sitter (AdS) space, mapping operators in the bulk of AdS, represented by logical qudits, onto operators on the boundary of the corresponding Conformal Field Theory (CFT), represented by physical qudits.
   Encoding can often be represented by a tensor network associated with a tiling of hyperbolic space.
@@ -39,7 +41,7 @@ features:
     - 'Holographic codes are argued to have a \textit{algebraic threshold}, for which the error rate scales polynomially (as opposed to exponentially) in the thermodynamic limit \cite{arxiv:2202.04710}. Such a threshold is governed by the underlying conformal field theory describing the boundary.'
 
 notes:
-  - 'All Boundary global symmetries must be dual to bulk gauge symmetries, and vice versa \cite{arxiv:1810.05338}.'
+  - 'Review of holographic tensor network codes \cite{arXiv:2102.02619}.'
 
 
 relations:
@@ -54,6 +56,10 @@ relations:
   cousins:
     - code_id: approximate_qecc
       detail: 'Universal subspace approximate error correction is used to model black holes \cite{arxiv:1807.06041}.'
+    - code_id: random_stabilizer
+      detail: 'Random holographic tensor-network codes reproduce many aspects of holography \cite{arxiv:1601.01694,arXiv:1801.05289,arxiv:2105.12067}.'
+    - code_id: hamiltonian
+      detail: 'Local Hamiltonians lying at the CFT boundary can be mapped into the AdS bulk using tools from Hamiltonian simulation theory \cite{arxiv:1810.08992}.'
 
 
 

codes/quantum/qubits/small_distance/small/stab_5_1_2.yml

@@ -26,11 +26,11 @@ relations:
   parents:
     - code_id: rotated_surface
     - code_id: holographic_5_1_2
-      detail: 'The \([[5,1,2]]\) rotated surface code is the smallest \([[5,1,2]]\)-pentagon holographic code.
-      The encoding of more general \([[5,1,2]]\)-pentagon holographic codes is a holographic tensor network consisting of encoding isometries for the \([[5,1,2]]\) rotated surface code, which are block-perfect tensors.'
+      detail: 'The \([[5,1,2]]\) rotated surface code is the smallest SCF holographic code.
+      The encoding of more general SCF holographic codes is a holographic tensor network consisting of encoding isometries for the \([[5,1,2]]\) rotated surface code, which are block-perfect tensors.'
     - code_id: block_perfect
-      detail: 'The \([[5,1,2]]\) rotated surface code is the smallest \([[5,1,2]]\)-pentagon holographic code.
-      The encoding of more general \([[5,1,2]]\)-pentagon holographic codes is a holographic tensor network consisting of encoding isometries for the \([[5,1,2]]\) rotated surface code, which are block-perfect tensors.'
+      detail: 'The \([[5,1,2]]\) rotated surface code is the smallest SCF holographic code.
+      The encoding of more general SCF holographic codes is a holographic tensor network consisting of encoding isometries for the \([[5,1,2]]\) rotated surface code, which are block-perfect tensors.'
     - code_id: small_distance_quantum
   cousins:
     - code_id: steane

codes/quantum/qubits/small_distance/small/stab_6_1_3.yml

@@ -26,6 +26,9 @@ features:
 relations:
   parents:
     - code_id: qubit_stabilizer
+    - code_id: holographic_6_1_3
+      detail: 'The \([[6,1,3]]\) six-qubit stabilizer code is the smallest six-qubit-tensor holographic code.
+      The encoding of more general SCF holographic codes is a holographic tensor network consisting of encoding isometries for the \([[6,1,3]]\) six-qubit stabilizer code.'
     - code_id: small_distance_quantum
   cousins:
     - code_id: subsystem_stabilizer

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

@@ -13,8 +13,9 @@ introduced: '\cite{arxiv:1503.06237}'
 
 description: |
   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}.
+  It has been generalized to higher dimensions \cite{arxiv:2112.12468} and to include gauge-like degrees of freedom on the links of the tensor network \cite{arxiv:1611.05841,arxiv:2108.11402}.
+  All boundary global symmetries must be dual to bulk gauge symmetries, and vice versa \cite{arxiv:1810.05338}.
 
   The construction below is described for qubits, but straightforward generalizations exist to modular qudits, oscillators, and rotors \cite{arxiv:1902.07714}.
   Encoding is accomplished using a tensor network of five-qubit encoding isometries, which are six-legged \hyperref[topic:ame]{perfect tensors} (with five legs corresponding to the physical qubits and one for the encoded logical qubit).

codes/quantum/qubits/stabilizer/holographic/holographic_5_1_2.yml

@@ -18,11 +18,12 @@ description: |
 
 
 features:
-  threshold:
-    - '\(7.1\%\) and \(8.2\%\) for even and odd raddi reduced-rate codes, respectively, under depolarising using the integer optimization decoder \cite{arxiv:2008.10206}'
+  code_capacity_threshold:
+    - '\(7.1\%\) and \(8.2\%\) for even and odd raddi reduced-rate codes, respectively, under depolarising using the integer optimization decoder \cite{arxiv:2008.10206}.'
 
 relations:
   parents:
+    - code_id: qubit_css
     - code_id: holographic_tensor
       detail: 'The encoding of the heptagon holographic code is a holographic tensor network consisting of encoding isometries for the \([[5,1,2]]\) rotated surface code, which are block-perfect tensors.'
   cousins:

codes/quantum/qubits/stabilizer/holographic/holographic_6_1_3.yml

@@ -0,0 +1,34 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: holographic_6_1_3
+physical: qubits
+logical: qubits
+
+name: 'Six-qubit-tensor holographic code'
+introduced: '\cite{arxiv:2009.10329}'
+
+description: |
+  Holographic tensor-network code constructed out of a network of encoding isometries of the \([[6,1,3]]\) six-qubit stabilizer code.
+  The structure of the isometry is similar to that of the heptagon holographic code since both isometries are rank-six tensors, but the isometry in this case is neither a \hyperref[topic:ame]{perfect tensor} nor a block-perfect tensor.
+
+
+features:
+  code_capacity_threshold:
+    - '\(18.8\%\) under depolarising using tensor-network decoder \cite{arxiv:2009.10329}.'
+
+relations:
+  parents:
+    - code_id: qubit_stabilizer
+    - code_id: holographic_tensor
+      detail: 'The encoding of the six-qubit-tensor holographic code is a holographic tensor network consisting of encoding isometries for the \([[6,1,3]]\) six-qubit stabilizer code.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-07-01'

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

@@ -27,6 +27,7 @@ features:
 
 relations:
   parents:
+    - code_id: qubit_css
     - 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:

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

@@ -0,0 +1,39 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: holographic_subsystem
+physical: qubits
+logical: qubits
+
+name: 'Holographic hybrid code'
+introduced: '\cite{arxiv:2010.05960}'
+
+alternative_names:
+  - 'Subsystem holographic code'
+
+description: |
+  Holographic tensor-network code constructed out of alternating isometries of the five-qubit and \([[4,1,1,2]]\) Bacon-Shor codes.
+
+
+relations:
+  parents:
+    - code_id: subsystem_stabilizer
+      detail: 'The holographic hybrid code is constructed out of alternating isometries of the five-qubit and \([[4,1,1,2]]\) Bacon-Shor codes.'
+    - code_id: holographic_tensor
+      detail: 'The holographic hybrid code is constructed out of alternating isometries of the five-qubit and \([[4,1,1,2]]\) Bacon-Shor codes.'
+  cousins:
+    - code_id: stab_5_1_3
+      detail: 'The holographic hybrid code is constructed out of alternating isometries of the five-qubit and \([[4,1,1,2]]\) Bacon-Shor codes.'
+    - code_id: bacon_shor
+      detail: 'The holographic hybrid code is constructed out of alternating isometries of the five-qubit and \([[4,1,1,2]]\) Bacon-Shor codes.'
+
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-07-01'