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errorcorrectionzoo · Jul 31, 2024 · a08ab7a · a08ab7a
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diff --git a/codes/classical/properties/block/distributed_storage/ldc.yml b/codes/classical/properties/block/distributed_storage/ldc.yml
@@ -37,6 +37,8 @@ relations:
   cousins:
     - code_id: ltc
       detail: 'There are relations between LDCs and LTCs \cite{doi:10.1007/978-3-642-15369-3_50}.'
+    - code_id: quantum_locally_recoverable
+      detail: 'There are quantum versions of LDCs, but they can be transformed into LDCs which can be decoded well on average \cite{arxiv:0806.2101}.'
 
 
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diff --git a/codes/quantum/properties/asymmetric_qecc.yml b/codes/quantum/properties/asymmetric_qecc.yml
@@ -75,9 +75,9 @@ relations:
     - code_id: quantum_reed_muller
       detail: 'Asymmetric quantum RM codes have been constructed \cite[Lemma 4.1]{doi:10.1098/rspa.2008.0439}.'
     - code_id: galois_bch
-      detail: 'Asymmetric quantum BCH codes have been constructed \cite[Lemma 4.4]{doi:10.1098/rspa.2008.0439}\cite{arxiv:quant-ph/0606107,doi:10.1109/ICCES.2008.4772987,doi:10.26421/QIC11.3-4-4}, including subsystem BCH codes \cite{arxiv:0803.0764}.'
+      detail: 'Asymmetric quantum BCH codes have been constructed \cite[Lemma 4.4]{doi:10.1098/rspa.2008.0439}\cite{arxiv:quant-ph/0606107,doi:10.1109/ICCES.2008.4772987,doi:10.26421/QIC11.3-4-4,arxiv:0804.4316}, including subsystem BCH codes \cite{arxiv:0803.0764}.'
     - code_id: pg_ldpc
-      detail: 'EG-LDPC codes can be used to construct asymmetric CSS codes \cite[Lemma 4.1]{doi:10.1098/rspa.2008.0439}.'
+      detail: 'FG-LDPC codes can be used to construct asymmetric CSS codes \cite[Lemma 4.1]{doi:10.1098/rspa.2008.0439}\cite{arxiv:0804.4316}.'
     - code_id: galois_polynomial
       detail: 'Asymmetric Galois-qudit RS codes have been constructed \cite{manual:{La Guardia, G. G., R. Palazzo, and C. Lavor. "Nonbinary quantum Reed-Solomon codes." Int. J. Pure Applied Math 65.1 (2010): 55-63.},doi:10.1007/s11128-011-0269-3}.'
     - code_id: bacon_shor

diff --git a/codes/quantum/qubits/qubit_concatenated.yml b/codes/quantum/qubits/qubit_concatenated.yml
@@ -31,6 +31,9 @@ relations:
   parents:
     - code_id: qubits_into_qubits
     - code_id: quantum_concatenated
+  cousins:
+    - code_id: hamiltonian
+      detail: 'Concatenated stabilizer code Hamiltonians have been investigated \cite{arxiv:0806.2160}.'
 
 
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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
@@ -61,7 +61,7 @@ features:
 
 
 realizations:
-  - '\([[4,1,2]]\) subcode implemented using four-qubit graph state of photons \cite{arxiv:1404.5498}.'
+  - '\([[4,1,2]]\) subcodes implemented in linear optical networks \cite{arxiv:0804.2268,arxiv:1404.5498}.'
   - 'Trapped-ion device by IonQ \cite{arxiv:1611.06946}.'
   - 'Logical state preparation and flag-qubit error correction realized in superconducting-circuit devices by IBM \cite{arxiv:1705.09259,arxiv:1705.08957,arxiv:1806.02359,arxiv:2110.04285}.'
   - 'The subcode \(\{|\overline{00}\rangle,|\overline{10}\rangle\}\) \cite{arxiv:1912.09410} and \(\{|\overline{00}\rangle,|\overline{01}\rangle\}\) \cite{arxiv:2102.06132}, treated as a planar surface code, has been realized in superconducting-circuit devices.'

diff --git a/codes/quantum/qudits_galois/stabilizer/bch/galois_bch.yml b/codes/quantum/qudits_galois/stabilizer/bch/galois_bch.yml
@@ -31,6 +31,8 @@ relations:
       detail: 'Galois-qudit BCH codes can be constructed via the CSS construction or the Hermitian construction.'
     - code_id: galois_subsystem_stabilizer
       detail: 'Asymmetric quantum BCH codes have been constructed \cite[Lemma 4.4]{doi:10.1098/rspa.2008.0439}\cite{arxiv:quant-ph/0606107,doi:10.1109/ICCES.2008.4772987,doi:10.26421/QIC11.3-4-4}, including subsystem BCH codes \cite{arxiv:0803.0764}.'
+    - code_id: qldpc
+      detail: 'Some Galois-qudit BCH codes can be constructed as QLDPC codes \cite{arxiv:0802.4079}.'
 
 
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