~

Author: valbert4

codes/quantum/qubits/small_distance/small/5/stab_5_1_3.yml

@@ -29,10 +29,14 @@ description: |
   A basis of codewords for the above stabilizer is \cite[Ch. 3]{preset:GottesmanBook}
   \begin{align}
   \begin{split}
-  |\overline{0}\rangle &= \tfrac{1}{4}(|00000\rangle + |10010\rangle + |01001\rangle - |11011\rangle + |10100\rangle - |00110\rangle - |11101\rangle - |01111\rangle \\
-  &\quad + |01010\rangle - |11000\rangle - |00011\rangle - |10001\rangle - |11110\rangle - |01100\rangle - |10111\rangle + |00101\rangle)\\
-  |\overline{1}\rangle &= \tfrac{1}{4}(|11111\rangle + |01101\rangle + |10110\rangle - |00100\rangle + |01011\rangle - |11001\rangle - |00010\rangle - |10000\rangle \\
-  &\quad + |10101\rangle - |00111\rangle - |11100\rangle - |01110\rangle - |00001\rangle - |10011\rangle - |01000\rangle + |11010\rangle)~.
+  |\overline{0}\rangle &= \tfrac{1}{4}(|00000\rangle + |10010\rangle + |01001\rangle - |11011\rangle \\
+  &\quad + |10100\rangle - |00110\rangle - |11101\rangle - |01111\rangle \\
+  &\quad + |01010\rangle - |11000\rangle - |00011\rangle - |10001\rangle \\
+  &\quad - |11110\rangle - |01100\rangle - |10111\rangle + |00101\rangle)\\
+  |\overline{1}\rangle &= \tfrac{1}{4}(|11111\rangle + |01101\rangle + |10110\rangle - |00100\rangle \\
+  &\quad + |01011\rangle - |11001\rangle - |00010\rangle - |10000\rangle \\
+  &\quad + |10101\rangle - |00111\rangle - |11100\rangle - |01110\rangle \\
+  &\quad - |00001\rangle - |10011\rangle - |01000\rangle + |11010\rangle)~.
   \end{split}
   \end{align}
   Logical Pauli operators are \(\bar{X} = XXXXX\) and \(\bar{Z} = ZZZZZ\) \cite[Table 3.4]{preset:GottesmanBook}.

codes/quantum/qubits/small_distance/small/8/qubit_8_4_2.yml

@@ -20,11 +20,12 @@ protection: |
 features:
   transversal_gates:
     - 'Even physical-qubit permutations act as \(GL(4,\mathbb{F}_2)\) on the logical basis, and odd permutations extend the permutation automorphism group to the full symmetric group \(S_8\) \cite{arxiv:2604.15111}.'
-    - '\(T^{\otimes 8}\) is a transversal non-Clifford gate implementing \(2\ketbra{\overline{0}}-\mathbbm{1}\) on the logical subspace \cite{arxiv:2604.15111}.'
+    - '\(T^{\otimes 8}\) is a transversal non-Clifford gate implementing \(2\ket{\overline{0}}\bra{\overline{0}}-I\) on the logical subspace \cite{arxiv:2604.15111}.'
     - 'A specific odd permutation implements a non-Clifford logical involution, and the full permutation automorphism group is \(S_8\) \cite{arxiv:2604.15111}.'
 
 relations:
   parents:
+    - code_id: qubits_into_qubits
     - code_id: small_distance_quantum
   cousins:
     - code_id: phantom

scripts/script_list_for_checking.txt

@@ -0,0 +1,7 @@
+redundant_direct_children
+redundant_primary_parent
+find_property_codes
+check_duplicate_relations
+spellcheck
+remove_trailing_block_apostrophes
+find_incorrect_description_first_paragraphs