quantum pin

codes/quantum/qubits/stabilizer/magic/quantum_k-orthogonal.yml

@@ -8,10 +8,12 @@ physical: qubits
 logical: qubits
 
 name: '\(k\)-orthogonal code'
-introduced: '\cite{arxiv:1503.08800,arXiv:2210.14066}'
+introduced: '\cite{arxiv:1503.08800,arxiv:1906.11394,arXiv:2210.14066}'
+# 1906.11394 also defines ell-orthogonal
 
 description: |
   Stabilizer code whose \(X\)-type generators form a \(k\)-orthogonal matrix (defined below) in the symplectic representation.
+  In other words, the overlap between any \(k\) stabilizers (including the identity) is even.
   This entry is formulated for qubits, but an extension exists for modular qudits \cite{arxiv:1503.08800}.
 
   A matrix is \(k\)-orthogonal \cite[Def. 4]{arxiv:2210.14066} if

codes/quantum/qubits/stabilizer/quantum_pin.yml

@@ -0,0 +1,36 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: quantum_pin
+physical: qubits
+logical: qubits
+
+name: 'Quantum pin code'
+introduced: '\cite{arXiv:1906.11394}'
+
+description: |
+  Member of a family of CSS codes that encompasses both quantum Reed-Muller and color codes and that is defined using intersections of pinned sets.
+
+features:
+  magic_scaling_exponent: 'A family of punctured pin codes admits \(\gamma \approx 1.6\) \cite[Table VII]{arxiv:1906.11394}.'
+
+
+relations:
+  parents:
+    - code_id: qubit_generalized_homological_product_css
+      detail: 'One can construct quantum pin codes from any chain complex \cite[Sec. II.F]{arxiv:1906.11394}.'
+    - code_id: quantum_k-orthogonal
+      detail: 'Quantum pin codes are \(\ell\)-orthogonal, i.e., the overlap between any \(\ell\) stabilizers is even \cite{arXiv:1906.11394}.'
+  cousins:
+    - code_id: subsystem_color
+      detail: 'Quantum pin codes have a subsystem version that can be viewed as a generalization of subsystem color codes \cite{arxiv:1906.11394}.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-03-14'

codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml

@@ -31,7 +31,8 @@ features:
 
 relations:
   parents:
-    - code_id: qubit_css
+    - code_id: quantum_pin
+      detail: 'Quantum Reed-Muller codes are special cases of quantum pin codes \cite[Sec. II.D]{arxiv:1906.11394}'
     - code_id: qudit_reed_muller
       detail: 'Prime-qudit RM codes reduce to quantum RM codes when \(q=p=2\).'
   cousins:

codes/quantum/qubits/stabilizer/topological/color/color.yml

@@ -45,7 +45,8 @@ features:
 
 relations:
   parents:
-    - code_id: qubit_generalized_homological_product_css
+    - code_id: quantum_pin
+      detail: 'Color codes are special cases of quantum pin codes \cite[Sec. II.E]{arxiv:1906.11394}'
   cousins:
     - code_id: higher_dimensional_surface
       detail: 'The color code on a \(D\)-dimensional closed manifold is equivalent to multiple decoupled copies of the \(D\)-dimensional surface code \cite{arxiv:1007.4601,arxiv:1503.02065,arXiv:1804.00866}.'