~

codes/classical/q-ary_digits/easy/q-ary_hamming.yml

@@ -30,7 +30,7 @@ relations:
     - code_id: bch
       detail: 'Some narrow sense BCH codes of length \(n=(q^r-1)/(q-1)\) such that \(\text{gcd}(r,q-1)=1\) are \(q\)-ary Hamming codes (\cite{doi:10.1017/CBO9780511807077}, Thm. 5.1.4).'
     - code_id: generalized_reed_muller
-      detail: 'Hamming codes are dual to first-order GRM codes (\cite{doi:10.1007/978-94-011-3810-9}, pg. 45).'
+      detail: '\(q\)-ary Hamming codes are dual to first-order GRM codes \cite[pg. 45]{doi:10.1007/978-94-011-3810-9}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/stabilizer/magic/quantum_k-orthogonal.yml

@@ -12,6 +12,7 @@ introduced: '\cite{arxiv:1503.08800,arXiv:2210.14066}'
 
 description: |
   Stabilizer code whose \(X\)-type generators form a \(k\)-orthogonal matrix (defined below) in the symplectic representation.
+  This entry is formulated for qubits, but an extension exists for modular qudits \cite{arxiv:1503.08800}.
 
   A matrix is \(k\)-orthogonal \cite[Def. 4]{arxiv:2210.14066} if
   \begin{align}
@@ -28,7 +29,7 @@ relations:
     - code_id: qubit_stabilizer
   cousins:
     - code_id: qudit_color
-      detail: '\(k\)-orthogonality can be extended to modular-qudit codes and is known as \(k^{\star}\)-orthogonality \cite[Def. 2]{arxiv:1503.08800}.
+      detail: 'The notion of \(k\)-orthogonality can be extended to modular-qudit codes and is known as \(k^{\star}\)-orthogonality \cite[Def. 2]{arxiv:1503.08800}.
       Modular-qudit color codes defined on lattices in \(D\) spatial dimension whose \(X\)-type stabilizers are placed on cells of dimension \(\nu \leq D\) are \(k^{\star}\)-orthogonal for all \(k \leq \nu\) \cite[Lemma 5]{arxiv:1503.08800}.'
 
 

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

@@ -12,7 +12,7 @@ short_name: 'LRESC'
 introduced: '\cite{arxiv:2309.11719}'
 
 description: |-
-  Code constructed using the hypergraph product of two copies of a concatanated LDPC-repetition code.
+  Code constructed using the hypergraph product of two copies of a concatenated LDPC-repetition code.
   This family interpolates between surface codes and hypergraph codes since the hypergraph product of two repetition codes yields the planar surface code.
 
 

codes/quantum/qubits/rm/quantum_reed_muller.yml → codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml

@@ -32,8 +32,6 @@ relations:
     - code_id: qubit_css
     - code_id: qudit_reed_muller
       detail: 'Prime-qudit RM codes reduce to quantum RM codes when \(q=p=2\).'
-    - code_id: galois_reed_muller
-      detail: 'Galois-qudit RM codes reduce to quantum RM codes when \(q=2\).'
   cousins:
     - code_id: reed_muller
     - code_id: quantum_convolutional

codes/quantum/qubits/stabilizer/topological/color/capped_color.yml → codes/quantum/qubits/subsystem/topological/color/capped_color.yml

@@ -25,7 +25,7 @@ features:
 
 relations:
   parents:
-    - code_id: color
+    - code_id: subsystem_color
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/subsystem/topological/color/doubled_color.yml

@@ -21,7 +21,7 @@ features:
 
 relations:
   parents:
-    - code_id: subsystem_css
+    - code_id: subsystem_color
     - code_id: translationally_invariant_subsystem
   cousins:
     - code_id: quantum_divisible

codes/quantum/qubits/subsystem/topological/color/subsystem_color.yml

@@ -7,18 +7,20 @@ code_id: subsystem_color
 physical: qubits
 logical: qubits
 
+# general class encapsulating capped and doubled, so not necessarily translation invariant. Consider peeling off original lattice codes to separate entries
 name: 'Subsystem color code'
 introduced: '\cite{arxiv:0908.4246,arxiv:1311.0879}'
 
 alternative_names:
   - 'Gauge color code'
 
 description: |
-  Subsystem version of the color code that is obtained by expanding the vertices of a two-colex embedded in a surface of genus \(g\).
+  A subsystem version of the color code.
+  One way to obtain it is by expanding the vertices of a two-colex embedded in a surface of genus \(g\).
   Vertex expansion consists of splitting every vertex into a triangle and splitting every edge into a pair of edges.
 
 protection: |
-  The family of subsystem codes has parameters \([[3m,2g,2m+2g-2,d]]\), where \(m\) is the number of vertices of the original embedded two-colex, where \(g\) is the genus of the surface embedding the two-colex, and where the distance is bounded from below by the length of the smallest nontrivial homological cycle of the two-colex \(\Gamma\) \cite[Construction B]{arxiv:1207.0479}\cite[Lemma 2]{arxiv:1805.12542}.
+  One family of subsystem codes has parameters \([[3m,2g,2m+2g-2,d]]\), where \(m\) is the number of vertices of the original embedded two-colex, where \(g\) is the genus of the surface embedding the two-colex, and where the distance is bounded from below by the length of the smallest nontrivial homological cycle of the two-colex \(\Gamma\) \cite[Construction B]{arxiv:1207.0479}\cite[Lemma 2]{arxiv:1805.12542}.
 
 features:
   general_gates:
@@ -38,13 +40,13 @@ relations:
     - code_id: subsystem_css
     - code_id: qudit_subsystem_color
       detail: 'Modular-qudit subsystem color codes reduce to subsystem color codes for \(q=2\).'
-    - code_id: translationally_invariant_subsystem
   cousins:
     - code_id: color
     - code_id: single_shot
       detail: 'The 3D subsystem color code is a single-shot code \cite{arxiv:1404.5504,arxiv:1503.08217}.'
     - code_id: symmetry_protected_self_correct
-      detail: 'A particular gauge-fixed version of this code on a 3D lattice yields a self-correcting memory protected by one-form symmetries (see Sec. IV D of Ref. \cite{arXiv:1805.01474}). The symmetric energy barrier grows linearly with the length of a side of the lattice. When the system is coupled locally to a thermal bath respecting the symmetry and below a critical temperature, the memory time grows exponentially with the side length.
+      detail: 'A particular gauge-fixed version of a subsystem code on a 3D lattice yields a self-correcting memory protected by one-form symmetries \cite[Sec. IV D]{arXiv:1805.01474}.
+      The symmetric energy barrier grows linearly with the length of a side of the lattice. When the system is coupled locally to a thermal bath respecting the symmetry and below a critical temperature, the memory time grows exponentially with the side length.
       The subsystem color code is not a self-correcting quantum memory if symmetry protection is removed \cite{arxiv:2305.06389}.'
 
 

codes/quantum/qudits/frobenius.yml

@@ -23,7 +23,7 @@ notes:
 
 relations:
   parents:
-    - code_id: qudit_stabilizer
+    - code_id: qudits_into_qudits
     - code_id: quantum_cyclic
 
 

codes/quantum/qudits/polynomial.yml → codes/quantum/qudits/stabilizer/ag/polynomial.yml

@@ -7,7 +7,7 @@ code_id: polynomial
 physical: qudits
 logical: qudits
 
-name: 'Prime-qudit quantum RS code'
+name: 'Prime-qudit RS code'
 introduced: '\cite{arxiv:quant-ph/9910059}'
 # doi:10.1103/PhysRevA.77.012308?
 
@@ -37,7 +37,7 @@ relations:
   parents:
     - code_id: qudit_css
     - code_id: galois_polynomial
-      detail: 'Galois-qudit RS codes for prime-dimensional qudits are quantum RS codes.'
+      detail: 'Galois-qudit RS codes for prime-dimensional qudits are prime-qudit RS codes.'
   cousins:
     - code_id: quantum_triorthogonal
       detail: 'Triorthogonality can be generalized to qudit codes.

codes/quantum/qudits/qudit_hamming_css.yml → codes/quantum/qudits/stabilizer/ag/qudit_hamming_css.yml

@@ -17,7 +17,8 @@ description: 'A family of CSS codes extending \hyperref[code:quantum_hamming_css
 
 relations:
   parents:
-    - code_id: qudit_css
+    - code_id: qudit_reed_muller
+      detail: '\([[2^r-1, 2^r-2r-1, 3]]_p\) quantum Hamming codes are constructed using \(q\)-ary Hamming codes, which themselves are dual to first-order GRM codes \cite[pg. 45]{doi:10.1007/978-94-011-3810-9}.'
     - code_id: small_distance_quantum
 
 

codes/quantum/qudits/small/qudit_reed_muller.yml → codes/quantum/qudits/stabilizer/ag/qudit_reed_muller.yml

@@ -10,8 +10,9 @@ logical: qudits
 name: 'Prime-qudit RM code'
 introduced: '\cite{arXiv:quant-ph/0502001,arxiv:1205.3104}'
 
+# Dual added to include qudit_hamming_css as a child
 description: |
-  Modular-qudit stabilizer code constructed from generalized Reed-Muller (GRM) codes via the modular-qudit CSS construction.
+  Modular-qudit stabilizer code constructed from generalized Reed-Muller (GRM) codes or their duals via the modular-qudit CSS construction.
   An odd-prime-qudit CSS code family constructed from first-order punctured RM codes transversally implements a diagonal gate at any level of the \hyperref[topic:qudit-clifford-hierarchy]{qudit Clifford hierarchy} \cite{arxiv:1205.3104}.
 
 features: