stab_6_1_3

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

@@ -0,0 +1,43 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: stab_6_1_3
+physical: qubits
+logical: qubits
+
+name: '\([[6,1,3]]\) six-qubit code'
+short_name: '\([[6,1,3]]\)'
+introduced: '\cite{arxiv:0803.1495}'
+
+description: |
+  One of two six-qubit distance-three codes that are unique up to equivalence \cite{arxiv:quant-ph/9608006}, with the other code a trivial extension of the five-qubit code \cite{arxiv:0803.1495}.
+  Stabilizer generators and logical Pauli operators are presented in Ref. \cite{arxiv:0803.1495}.
+
+features:
+  encoders:
+    - 'CNOT and Hadamard gates \cite{arxiv:0803.1495}.'
+  general_gates:
+    - 'Logical CNOT gate \cite{arxiv:0803.1495}.'
+
+
+relations:
+  parents:
+    - code_id: qubit_stabilizer
+    - code_id: small_distance_quantum
+  cousins:
+    - code_id: subsystem_stabilizer
+      detail: 'The \([[6,1,3]]\) six-qubit code can be converted into a \([[6,1,1,3]]\) subsystem code that saturates the subsystem Singleton bound \cite{arxiv:0803.1495}.'
+    - code_id: stab_5_1_3
+      detail: 'The \([[6,1,3]]\) six-qubit code is one of two six-qubit distance-three codes that are unique up to equivalence \cite{arxiv:quant-ph/9608006}, with the other code a trivial extension of the five-qubit code \cite{arxiv:0803.1495}.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-05-26'
+    - user_id: MatthewSteinberg
+      date: '2024-05-26'

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

@@ -12,7 +12,7 @@ short_name: 'Steane'
 introduced: '\cite{doi:10.1098/rspa.1996.0136}'
 
 description: |
-  A \([[7,1,3]]\) CSS code that is the smallest qubit CSS code to correct a single-qubit error.
+  A \([[7,1,3]]\) CSS code that is the smallest qubit CSS code to correct a single-qubit error \cite{arxiv:0803.1495}.
   The code is constructed using the classical binary \([7,4,3]\) Hamming code for protecting against both \(X\) and \(Z\) errors.
 
   The code's stabilizer generator matrix blocks \(H_{X}\) and \(H_{Z}\) are both the parity-check matrix for the \([7,4,3]\) Hamming code,
@@ -109,6 +109,8 @@ relations:
       detail: 'The Steane code is equivalent to a cyclic code via qubit permutations \cite[Exam. 1]{arxiv:1108.5490}.'
     - code_id: cws
       detail: 'The Steane code is equivalent via a single-qubit Clifford unitary to a CWS code for a particular graph and classical code \cite[Exam. 4]{arxiv:1108.5490}.'
+    - code_id: eastab
+      detail: 'The Steane code is globally equivalent to a \([[6,1,3;1]]\) code, which is the smallest EA CSS code with that distance \cite{arxiv:0803.1495}.'
 
 
 #      detail: 'Steane code is the smallest member of a family of Reed-Muller-based CSS codes.'

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

@@ -32,7 +32,7 @@ relations:
     - code_id: qubits_into_qubits
     - code_id: commuting_projector
     - code_id: topological
-      detail: 'Cubic theory codes realize \(\geq 5\)-dimensional higher-form \(\mathbb{Z}_2^3\) gauge theories with non-Abelian excitations.'
+      detail: 'Cubic theory codes realize higher-form \(\mathbb{Z}_2^3\) gauge theories with non-Abelian excitations in arbitrary dimensions.'
   cousins:
     - code_id: self_correct
       detail: 'A family of five-dimensional cubic theory codes with non-Abelian excitations is argued to be self-correcting below a critical temperature via a Peierls argument \cite{arxiv:2405.11719}.'

users/users_db.yml

@@ -36,6 +36,10 @@
 #
 
 
+- user_id: MatthewSteinberg
+  name: 'Matthew Steinberg'
+  gscholaruser: lGZwMRAAAAAJ
+
 - user_id: GuanyuZhu
   name: 'Guanyu Zhu'
   gscholaruser: 49-A-XQAAAAJ