subsystem refs

errorcorrectionzoo · Nov 20, 2023 · c7ea381 · c7ea381
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diff --git a/codes/quantum/qubits/small_distance/small/shor_nine.yml b/codes/quantum/qubits/small_distance/small/shor_nine.yml
@@ -70,6 +70,8 @@ relations:
       detail: 'The Shor code is a concatenation of a three-qubit bit-flip with a three-qubit phase-flip repetition code.'
     - code_id: quantum_concatenated
       detail: 'The Shor code is a concatenation of a three-qubit bit-flip with a three-qubit phase-flip repetition code.'
+    - code_id: bacon_shor
+      detail: 'The \([[9,1,3,3]]\) Bacon-Shor code reduces to the \hyperref[code:shor_nine]{Shor code} for a particular gauge configuration.'
     - code_id: qecc
       detail: 'The Shor code is the first quantum error-correcting code.'
 

diff --git a/codes/quantum/qubits/small_distance/small/stab_4_2_2.yml b/codes/quantum/qubits/small_distance/small/stab_4_2_2.yml
@@ -69,7 +69,7 @@ relations:
     - code_id: rotated_surface
       detail: 'Various \([[4,1,2]]\) subcodes are small rotated planar codes \cite{arxiv:2006.03071,arxiv:1912.09410,arXiv:2102.06132,arXiv:2102.13071}.'
     - code_id: bacon_shor
-      detail: 'The error-detecting \([[4,1,2]]\) Bacon-Shor code, which reduces to a subcode of the \hyperref[code:stab_4_2_2]{\([[4,2,2]]\) code} for a particular gauge configuration, has gauge operators \(\{XXII,IIXX,ZIZI,IZIZ\}\).'
+      detail: 'The error-detecting \([[4,1,1,2]]\) Bacon-Shor code, which reduces to a subcode of the \hyperref[code:stab_4_2_2]{\([[4,2,2]]\) code} for a particular gauge configuration, has gauge operators \(\{XXII,IIXX,ZIZI,IZIZ\}\).'
     - code_id: quantum_parity
       detail: '\([[4,1,2]]\) subcode \(\{|\overline{00}\rangle,|\overline{01}\rangle\}\) is the smallest member of the sub-family of \([[m^2,1,m]]\) QPC codes.'
     - code_id: stab_5_1_3

diff --git a/codes/quantum/qubits/subsystem/bacon_shor.yml b/codes/quantum/qubits/subsystem/bacon_shor.yml
@@ -24,7 +24,7 @@ description: |
   \end{align}
   Syndrome extraction can be done by measuring these gauge operators, which are on fewer qubits and local.
 
-  The shortest error-correcting Bacon-Shor code is \([[9,1,3]]\) with four stabilizer generators
+  The shortest error-correcting Bacon-Shor code is \([[9,1,3,3]]\), with four stabilizer generators
   \begin{align}
     \begin{array}{ccccccccc}
       X & X & X & X & X & X & I & I & I\\

diff --git a/codes/quantum/qubits/subsystem/subsystem_stabilizer.yml b/codes/quantum/qubits/subsystem/subsystem_stabilizer.yml
@@ -57,6 +57,10 @@ relations:
   cousins:
     - code_id: qubit_stabilizer
       detail: 'Subsystem stabilizer codes reduce to stabilizer codes when there are no gauge qubits.'
+    - code_id: q-ary_bch
+      detail: 'BCH codes yield subsystem stabilizer codes via the subsystem extension of the Hermitian construction \cite[Exam. 1]{arxiv:quant-ph/0610153}.'
+    - code_id: reed_solomon
+      detail: 'Primitive RS codes yield subsystem stabilizer codes via the subsystem extension of the Hermitian construction \cite[Exam. 3]{arxiv:quant-ph/0610153}.'
 
 
 # Begin Entry Meta Information

diff --git a/codes/quantum/qudits_galois/subsystem/galois_subsystem_stabilizer.yml b/codes/quantum/qudits_galois/subsystem/galois_subsystem_stabilizer.yml
@@ -14,6 +14,8 @@ description: |
   Galois-qudit generalization of a subsystem qubit stabilizer code.
   Can be obtained by taking a Galois-qudit stabilizer code and assigning some of its logical qubits to be gauge qubits.
 
+protection: |
+  Bounds on code parameters are formulated in Ref. \cite{arxiv:quant-ph/0610153}. 
 
 relations:
   parents: