kls

codes/quantum/qubits/small_distance/kls.yml

@@ -0,0 +1,41 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: kls
+physical: qubits
+logical: qubits
+
+name: '\([[m 2^m / (m+1), 2^m / (m+1)]]\) Khesin-Lu-Shor code'
+short_name: '\([[m 2^m / (m+1), 2^m / (m+1)]]\)'
+introduced: '\cite{arxiv:2411.14448}'
+
+description: |
+  A family of \([[m 2^m / (m+1), 2^m / (m+1)]]\) qubit CSS codes derived from the Hamming code.
+  Their \hyperref[topic:encoder-respecting]{encoder-respecting form} is the graph of a hypercube in \(m = 2^r - 1\) dimensions, and input nodes in the graph are codewords of the \([2^r-1,2^r-r-1,3]\) Hamming code \cite{arxiv:2411.14448}.
+
+protection: 'The code distance is bounded above and conjectured to be \(m\) \cite{arxiv:2411.14448}.'
+
+
+relations:
+  parents:
+    - code_id: qubit_css
+  cousins:
+    - code_id: hamming
+      detail: 'The \hyperref[topic:encoder-respecting]{encoder-respecting form} of the \([[m 2^m / (m+1), 2^m / (m+1)]]\) Khesin-Lu-Shor code is the graph of a hypercube in \(m = 2^r - 1\) dimensions, and input nodes in the graph are codewords of the \([2^r-1,2^r-r-1,3]\) Hamming code \cite{arxiv:2411.14448}.'
+    - code_id: hypercube
+      detail: 'The \hyperref[topic:encoder-respecting]{encoder-respecting form} of the \([[m 2^m / (m+1), 2^m / (m+1)]]\) Khesin-Lu-Shor code is the graph of a hypercube in \(m = 2^r - 1\) dimensions, and input nodes in the graph are codewords of the \([2^r-1,2^r-r-1,3]\) Hamming code \cite{arxiv:2411.14448}.'
+    - code_id: steane
+      detail: 'The \hyperref[topic:encoder-respecting]{encoder-respecting form} of both the Steane and Khesin-Lu-Shor codes is the graph of a hypercube \cite{arxiv:2411.14448}.'
+
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-12-11'
+    - user_id: AndreyBorisKhesin
+      date: '2024-12-11'

codes/quantum/qubits/small_distance/small/6/stab_6_2_2.yml

@@ -24,7 +24,8 @@ features:
 
 relations:
   parents:
-    - code_id: qubit_css
+    - code_id: kls
+      detail: 'The Khesin-Lu-Shor code for \(r=2\) and \(m=2^r - 1 = 3\) is the \([[6,2,2]]\) \(C_6\) code.'
     - code_id: small_distance_quantum
   cousins:
     - code_id: qubit_concatenated

users/users_db.yml

@@ -33,6 +33,11 @@
 # Code Contributors -- leave out 'zooteam:'.
 
 #
+
+- user_id: AndreyBorisKhesin
+  name: 'Andrey Boris Khesin'
+  githubusername: AndreyBorisKhesin
+
 - user_id: DavidTStephen
   name: 'David T. Stephen'
   gscholaruser: KBuD0aMAAAAJ