lresc lacross detail

codes/quantum/qubits/stabilizer/qldpc/concatenated/lacross.yml

@@ -11,14 +11,16 @@ name: 'La-cross code'
 introduced: '\cite{arxiv:2404.13010}'
 
 description: |-
-  Code constructed using the hypergraph product of two copies of an LDPC seed code.
+  Code constructed using the hypergraph product of two copies of a cyclic LDPC code.
   The construction uses cyclic LDPC codes with \hyperref[topic:Cyclic-to-polynomial-correspondence]{generating polynomials} \(1+x+x^k\) for some \(k\).
   Using a length-\(n\) seed code yields an \([[2n^2,2k^2]]\) family for periodic boundary conditions and an \([[(n-k)^2+n^2,k^2]]\) family for open boundary conditions.
 
 
 relations:
   parents:
     - code_id: hypergraph_product
+      detail: 'La-cross codes are constructed using the hypergraph product a cyclic LDPC code with itself.'
+    - code_id: quantum_cyclic
 
 
 _meta:

codes/quantum/qubits/stabilizer/qldpc/concatenated/lresc.yml

@@ -12,15 +12,23 @@ short_name: 'LRESC'
 introduced: '\cite{arxiv:2309.11719}'
 
 description: |-
-  Code constructed using the hypergraph product of two copies of a particular concatenated LDPC-repetition code.
+  Code constructed using the hypergraph product of two copies of a concatenated LDPC-repetition seed code.
   This family interpolates between surface codes and hypergraph codes since the hypergraph product of two repetition codes yields the planar surface code.
   The construction uses small \([3,2,2]\) and \([6,2,4]\) LDPC codes concatenated with \([4,1,4]\) and \([2,1,2]\) repetition codes, respectively.
   An example using a \([5,2,3]\) code is also presented.
 
+features:
+  general_gates:
+    - 'Patch-transversal gates for suitable seed codes \cite{arxiv:2309.11719}.'
+
 relations:
   parents:
+    - code_id: hypergraph_product
+      detail: 'LRESCs are constructed using the hypergraph product a concatenated LDPC-repetition code with itself.'
+  cousins:
     - code_id: lacross
-      detail: 'La-cross codes reduce to LRESCs for \(k=2\).'
+      detail: 'La-cross codes yield LRESCs for \(k=2\).
+      La-cross codes have a number of long-range stabilizers that scales linearly with code size, while the number of LRESC long-range stabilizers can be tuned to scale between the square-root of the size and linearly in the size.'
 
 
 _meta:

codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface/surface.yml

@@ -202,6 +202,8 @@ relations:
       detail: 'Layer codes are combinations of constant-rate QLDPC codes with surface codes built using lattice surgery.'
     - code_id: lresc
       detail: 'LRESCs reduce to planar surface codes when a trivial LDPC code is used in the hypergraph product.'
+    - code_id: lacross
+      detail: 'La-cross codes at \(k=1\) yield the toric (planar surface) code and periodic (open) boundary conditions.'
     - code_id: majorana_stab
       detail: 'The Majorana mapping can be used to construct efficient algorithms for simulating rounds of error correction for the surface code \cite{arxiv:1710.02270}.'
     - code_id: quantum_double