equivalance check

Author: valbert4

codes/quantum/qubits/small_distance/small/13/quad_residue_13_1_5.yml

@@ -9,12 +9,10 @@ logical: qubits
 
 name: '\([[13,1,5]]\) quantum QR code'
 introduced: '\cite[pg. 11]{arxiv:quant-ph/9704019}'
-# qecdb id 67067199e766ad364e845262
-
 
 description: |
   Thirteen-qubit cyclic Hermitian qubit code derived from a quaternary quadratic-residue code using the Hermitian construction \cite[pg. 11]{arxiv:quant-ph/9704019}\cite{arxiv:2211.00891}.
-  The code admits a stabilizer tableau whose rows are cyclic permutations of the Pauli string \(XXZZIZIIIZIZZ\).
+  The code admits a stabilizer tableau whose rows are cyclic permutations of the Pauli string \(XXZZIZIIIZIZZ\) \cite[ID 67067199e766ad364e845262]{preset:qecdb}.
 
 
 relations:

codes/quantum/qubits/small_distance/small/15/stab_15_1_3.yml

@@ -27,7 +27,7 @@ description: |
 
   The code can also be thought of as a code on all corners of a tesseract except one \cite{doi:10.1098/rsta.2011.0494}.
 
-  In the qubit order given by the nonzero binary four-tuples \(0001,0010,\ldots,1111\), one stabilizer tableau for the code is
+  In the qubit order given by the nonzero binary four-tuples \(0001,0010,\ldots,1111\), one stabilizer tableau for the code is \cite[ID 6705228b19cca60cf657a8f6]{preset:qecdb}
   \begin{align}
   \begin{smallmatrix}
     Z & Z & I & Z & I & I & Z & I & I & I & I & I & I & I & I \\

codes/quantum/qubits/small_distance/small/15/stab_15_7_3.yml

@@ -16,7 +16,7 @@ description: |
   Self-dual quantum Hamming code that admits permutation-based CZ logical gates.
   The code is constructed using the CSS construction from the \([15,11,3]\) Hamming code and its \([15,4,8]\) dual simplex code.
 
-  In the qubit order given by the nonzero binary four-tuples \(0001,0010,\ldots,1111\), one stabilizer tableau for the code is
+  In the qubit order given by the nonzero binary four-tuples \(0001,0010,\ldots,1111\), one stabilizer tableau for the code is \cite[ID 6705229219cca60cf657a8fd]{preset:qecdb}
   \begin{align}
   \begin{smallmatrix}
     I & I & I & I & I & I & I & Z & Z & Z & Z & Z & Z & Z & Z \\
@@ -44,6 +44,8 @@ features:
 relations:
   parents:
     - code_id: quantum_hamming_css
+    - code_id: stabilizer_over_gf4
+      detail: 'The \([[15,7,3]]\) is Hermitian \cite[ID 6705229219cca60cf657a8fd]{preset:qecdb}.'
   cousins:
     - code_id: quantum_perfect
       detail: '\([[15, 7, 3]]\) quantum Hamming code is perfect as a CSS code, i.e., the number of its \(Z\)-type syndromes matches the number of \(X\)-type Pauli errors up to weight one \cite{arxiv:1705.05365}.'

codes/quantum/qubits/small_distance/small/20/stab_20_2_6.yml

@@ -43,6 +43,7 @@ description: |
   \end{smallmatrix}~.
   \end{align}
   Rows 1--5 are the \(Z\)-type inner stabilizers of each \([[4,2,2]]\) block; rows 6--9 are the lifted outer \(Z\)-type stabilizers; rows 10--14 are the \(X\)-type inner stabilizers; rows 15--18 are the lifted outer \(X\)-type stabilizers.
+  This code is equivalent, up to qubit permutations and single-qubit Clifford gates, to three \([[20,2,6]]\) self-dual CSS codes in QECDB \cite[ID 672e6e9c34d5954e0cb7d1b7]{preset:qecdb}\cite[ID 67a388ef9d65c7b409826879]{preset:qecdb}\cite[ID 67a3890a9d65c7b40982687b]{preset:qecdb}.
 
 protection: |
   Detects errors on up to 5 qubits and corrects errors on up to 2 qubits.