minor corrections + refs

codes/quantum/properties/block/quantum_mds.yml

@@ -9,15 +9,23 @@ code_id: quantum_mds
 
 name: 'Quantum maximum-distance-separable (MDS) code'
 short_name: 'Quantum MDS'
-introduced: '\cite{arxiv:quant-ph/9702031}'
+introduced: '\cite{arxiv:quant-ph/9702031,arxiv:quant-ph/9703048}'
 
 description: |
-  An \(((n,q^k,d))\) code constructed out of \(q\)-dimensional qudits is an MDS code if parameters \(n\), \(k\), \(d\), and \(q\) are such that the quantum Singleton bound
+  An \(((n,K,d))\) code constructed out of \(q\)-dimensional qubits or Galois qudits is an MDS code if parameters \(n\), \(k\), \(d\), and \(q\) are such that the quantum Singleton bound
   \begin{align}
-  2(d-1) \leq n-k
+  K \leq q^{n-2(d-1)}
   \end{align}
   becomes an equality.
-  Such codes are pure \cite{arxiv:1907.07733}.
+  When \(K = q^k\) for some integer \(k\), the above reduces to \(2(d-1) \leq n-k\).
+  Such codes are pure \cite{arxiv:quant-ph/9703048}.
+
+# An \(((n,q^k,d))\) code constructed out of \(q\)-dimensional qudits is an MDS code if parameters \(n\), \(k\), \(d\), and \(q\) are such that the quantum Singleton bound
+# \begin{align}
+# 2(d-1) \leq n-k
+# \end{align}
+# becomes an equality.
+# Such codes are pure \cite{arxiv:quant-ph/9703048}.
 
 protection: 'Given \(n\) and \(k\), MDS codes have the highest distance possible of all codes and so have the best possible error correction properties.'
 

codes/quantum/qubits/small_distance/quantum_hamming.yml

@@ -7,11 +7,14 @@ code_id: quantum_hamming
 physical: qubits
 logical: qubits
 
-name: '\([[2^r, 2^r-r-2, 3]]\) quantum Hamming code'
+name: 'Gottesman code'
 short_name: '\([[2^r, 2^r-r-2, 3]]\)'
 introduced: '\cite{arXiv:quant-ph/9604038}'
 
-description: 'A family of stabilizer codes of distance \(3\) that saturate the asymptotic quantum Hamming bound. Can be obtained from the CSS construction using a first-order \([2^r,r+1,2^{r-1}]\) RM code and a \([2^r,2^r-1,2]\) even-weight code \cite{arxiv:quant-ph/9605021}.'
+alternative_names:
+  - '\([[2^r, 2^r-r-2, 3]]\) quantum Hamming code'
+
+description: 'A family of stabilizer codes of distance \(3\) that saturate the asymptotic quantum Hamming bound. Can be obtained from the CSS construction with a \([2^r,r+1,2^{r-1}] = C_2^{\perp}\) RM code and a \([2^r,2^r-1,2] = C_1\) even-weight code \cite{arxiv:quant-ph/9605021}.'
 
 protection: 'Protects against any single qubit error.'
 

codes/quantum/qubits/stabilizer/qubit_css.yml

@@ -92,6 +92,8 @@ protection: |
 
   The distance of the CSS code is equal to the minimum of the combinatorial (\(d-1\))-systole of the cellulated \(d\)-dimensional manifold and its dual.
 
+  CSS codes have a \textit{CSS lower bound} against depolarizing noise, quantified by lower bounds on independently decoding the two classical codes \cite{doi:10.1109/ISIT.2013.6620358}.
+
 features:
   rate: 'For a depolarizing channel with probability \(p\), CSS codes allowing for arbitrarily accurate recovery exist with asymptotic rate \(1-2h(p)\), where \(h\) is the binary entropy function \cite{arxiv:quant-ph/0110143}.'
   encoders:

codes/quantum/qubits/stabilizer/topological/surface/higher_dim_surface/3d_surface.yml

@@ -22,6 +22,8 @@ description: |
   The construction on surfaces with boundaries is often called the
   \textit{3D surface code}.
 
+  Related models \cite{arxiv:cond-mat/0607736,arxiv:1012.0859} on lattices with certain colorability are equivalent to several copies of the 3D surface code \cite{arXiv:1908.08049}.
+
 
 protection: |
   The planar 3D surface code family on a cubic lattice of length \(L\) has parameters \([[2L(L-1)^2+L^3,1,d_X=L^2,d_Z=L]]\), while the 3D toric code has parameters \([[3L^3,3,d_X=L^2,d_Z=L]]\).

codes/quantum/qudits_galois/stabilizer/stabilizer_over_gfqsq.yml

@@ -8,7 +8,7 @@ physical: galois
 logical: galois
 
 name: 'Hermitian-construction code'
-introduced: '\cite{arXiv:quant-ph/0508070}'
+introduced: '\cite{doi:10.1109/18.959288,arXiv:quant-ph/0508070}'
 
 # alternative_names:
 #   - 'Stabilizer code over \(GF(q^2)\)'