ampdamp_numopt

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

@@ -0,0 +1,45 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: ampdamp_numopt
+physical: qubits
+logical: qubits
+
+name: 'Numerically optimized four-qubit AD code'
+introduced: '\cite{arxiv:2411.12952}'
+
+description: |
+  Four-qubit code that can (approximately) correct a single \hyperref[topic:ad]{AD} error with higher entanglement fidelity than the \([[4,1,2]]\) subcodes of the \([[4,2,2]]\) code.
+  The code was obtained by a biconvex optimization of the entanglement fidelity.
+
+  The admits a codeword basis of
+  \begin{align}
+  \begin{split}
+  |\overline{0}\rangle&=\sqrt{1-\frac{1}{2(1-\gamma)^{2}}}|0000\rangle+\frac{1}{\sqrt{2}(1-\gamma)}|1111\rangle\\|\overline{1}\rangle&=\frac{1}{2}(|0011\rangle+|0101\rangle-|1010\rangle+|1100\rangle)\end{split}
+  \end{align}
+  for \hyperref[topic:ad]{AD} error rate \(\gamma\).
+
+features:
+  encoders:
+    - 'Analytical encoding channel \cite{arxiv:2411.12952}.'
+  decoders:
+    - 'Analytical recovery channel \cite{arxiv:2411.12952}.'
+
+relations:
+  parents:
+    - code_id: qubits_into_qubits
+    - code_id: ampdamp
+    - code_id: small_distance_quantum
+  cousins:
+    - code_id: stab_4_2_2
+      detail: 'The numerically optimized four-qubit AD code that can correct a single \hyperref[topic:ad]{AD} error with higher entanglement fidelity than the \([[4,1,2]]\) Leung-Nielsen-Chuang-Yamamoto code subcode of the \([[4,2,2]]\) code.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-11-21'

codes/quantum/qubits/small_distance/small/stab_4_2_2.yml

@@ -29,7 +29,7 @@ description: |
   This code is the smallest instance of the toric code, and its various single-qubit subcodes are small planar surface codes.
   It is the unique code for its parameters, up to equivalence \cite[Thm. 8]{arxiv:quant-ph/9704043}.
 
-  The subcode \(\{|\overline{00}\rangle,|\overline{01}\rangle\}\) is a \([[4,1,2]]\) code \cite{arxiv:quant-ph/9704002}, whose \(\pm\)-basis codewords can be written as
+  The subcode \(\{|\overline{00}\rangle,|\overline{01}\rangle\}\) is a \([[4,1,2]]\) code known as the \textit{Leung-Nielsen-Chuang-Yamamoto code} \cite{arxiv:quant-ph/9704002}, whose \(\pm\)-basis codewords can be written as
   \begin{align}
     |\overline{\pm}\rangle = \frac{1}{2}(|00\rangle \pm |11\rangle)^{\otimes 2}~.\\
   \end{align}
@@ -103,7 +103,7 @@ relations:
     - code_id: stab_5_1_3
       detail: 'The \([[4,2,2]]\) code can be derived from the five-qubit code using a protocol that converts an \([[n,k,d]]\) code into an \([[n-1, k+1, d-1]]\) code \cite[Sec. 3.5]{arxiv:quant-ph/9705052}.'
     - code_id: ampdamp
-      detail: 'The \([[4,1,2]]\) subcode \(\{|\overline{00}\rangle,|\overline{10}\rangle\}\) (approximately) corrects a single \hyperref[topic:ad]{AD} error \cite{arxiv:quant-ph/9704002}.'
+      detail: 'The \([[4,1,2]]\) Leung-Nielsen-Chuang-Yamamoto subcode \(\{|\overline{00}\rangle,|\overline{10}\rangle\}\) (approximately) corrects a single \hyperref[topic:ad]{AD} error \cite{arxiv:quant-ph/9704002}.'
     - code_id: binomial
       detail: '\([[4,1,2]]\) subcode consisting of \(|\overline{00}\rangle\) and any other codeword reduces to the \(0,2,4\) binomial code when the basis labels in each codeword are written as in base-ten.
       Such a mapping can be generalized \cite{manual:{Linshu Li, private communication, 2018}}.'