make BPT a term

codes/classical/bits/quantum_inspired/newman_moore.yml

@@ -14,7 +14,7 @@ description: |
   Member of a family of \([L^2,O(L),O(L^{\frac{\log 3}{\log 2}})]\) binary linear codes on \(L\times L\) square lattices that form the ground-state subspace of a class of exactly solvable spin-glass models with three-body interactions.
   The codewords resemble the Sierpinski triangle on a square lattice, which can be generated by a cellular automaton \cite{doi:10.1109/12.286310}.
 
-protection: 'Code parameters nearly saturate the classical version of the BPT bound, based on numerical simulations and analytical arguments \cite[Appx. A]{arxiv:0909.5200}.'
+protection: 'Code parameters nearly saturate the classical version of the \hyperref[topic:BPT-bound]{BPT bound}, based on numerical simulations and analytical arguments \cite[Appx. A]{arxiv:0909.5200}.'
 
 features:
   decoders:

codes/classical/q-ary_digits/quantum_inspired/classical_fractal_liquid.yml

@@ -13,7 +13,7 @@ introduced: '\cite{arXiv:1111.3275,arxiv:1302.6248}'
 description: |
   Member of a family of \([L^D,O(L^{D-1}),O(L^{D-\epsilon})]_p\) linear codes on \(D\)-dimensional square lattices of side length \(L\) and for some prime \(p\) and \(\epsilon > 0\) that is based on \(p\)-ary generalizations of the Sierpinski triangle.
 
-protection: 'Parameters of some code families saturate the classical version of the BPT bound \cite{arxiv:1111.3275}.'
+protection: 'Parameters of some code families saturate the classical version of the \hyperref[topic:BPT-bound]{BPT bound} \cite{arxiv:1111.3275}.'
 
 
 relations:

codes/quantum/properties/stabilizer/qldpc/good_qldpc.yml

@@ -34,7 +34,7 @@ relations:
     - code_id: qldpc
   cousins:
     - code_id: translationally_invariant_stabilizer
-      detail: 'Chain complexes describing some good QLDPC codes can be ''lifted'' into higher-dimensional manifolds admitting some notion of geometric locality \cite{arXiv:2012.02249,arxiv:2309.16104}. Applying this procedure to good QLDPC codes yiels \([[n,n^{1-2/D},n^{1-1/D}]]\) lattice stabilizer codes in \(D\) spatial dimensions that saturate the BPT bound, up to corrections poly-logarithmic in \(n\) \cite{arxiv:2303.06755}.'
+      detail: 'Chain complexes describing some good QLDPC codes can be ''lifted'' into higher-dimensional manifolds admitting some notion of geometric locality \cite{arXiv:2012.02249,arxiv:2309.16104}. Applying this procedure to good QLDPC codes yiels \([[n,n^{1-2/D},n^{1-1/D}]]\) lattice stabilizer codes in \(D\) spatial dimensions that saturate the \hyperref[topic:BPT-bound]{BPT bound}, up to corrections poly-logarithmic in \(n\) \cite{arxiv:2303.06755}.'
 
 
 # Begin Entry Meta Information

codes/quantum/properties/stabilizer/topological_stabilizer/translationally_invariant_stabilizer.yml

@@ -39,9 +39,12 @@ description: |
 #  equivalently expressed by the Laurent polynomial \(x_1x_2^2x_3^3e_1 + x_1^{-1}x_2^2x_3^4e_{q+2}\).
 
 protection: |
+    \begin{defterm}{BPT bound}
+    \label{topic:BPT-bound}
     Lattice qubit codes are limited by the \textit{Bravyi-Poulin-Terhal (BPT) bound} \cite{arxiv:0909.5200} (see also \cite{arxiv:0810.1983,arxiv:1008.1029,arxiv:1610.06169}), which states that \(d \leq O(n^{1-1/D})\) and \(k d^{2/D-1} = O(n)\) for \(D\)-dimensional lattice geometries.
     The \textit{Bravyi-Terhal (BT) bound} states that \(d = O(L^{D-1})\) \cite{arxiv:0810.1983}.
     Codes on a \(D\)-dimensional homogeneous Riemannian manifold with diameter \(L\) satisfy \(k = O(L^{D-2})\) \cite{arxiv:2009.13551}.
+    \end{defterm}
 
 
 features:

codes/quantum/qubits/stabilizer/topological/surface/higher_dim_surface/layer.yml

@@ -15,7 +15,7 @@ description: |
   Geometric locality is maintained because, instead of being concatenated, each pair of parallel surface-code squares are fused (or quasi-concatenated) with perpendicular surface-code squares via lattice surgery.
 
 features:
-  rate: 'Code parameters on a cube, \([[n,\Theta(n^{1/3}),\Theta(n^{1/3})]]\), achieve the 3D BPT bound when asymptotically good QLDPC codes are used in the construction.'
+  rate: 'Code parameters on a cube, \([[n,\Theta(n^{1/3}),\Theta(n^{1/3})]]\), achieve the 3D \hyperref[topic:BPT-bound]{BPT bound} when asymptotically good QLDPC codes are used in the construction.'
 
 
 relations:
@@ -27,7 +27,7 @@ relations:
       detail: 'The Layer code realizes 2D layers of \(\mathbb{Z}_2\) gauge theory connected by defects.'
   cousins:
     - code_id: good_qldpc
-      detail: 'Layer code parameters, \([[n,\Theta(n^{1/3}),\Theta(n^{1/3})]]\), achieve the BPT bound in 3D when asymptotically good QLDPC codes are used in the construction.'
+      detail: 'Layer code parameters, \([[n,\Theta(n^{1/3}),\Theta(n^{1/3})]]\), achieve the \hyperref[topic:BPT-bound]{BPT bound} in 3D when asymptotically good QLDPC codes are used in the construction.'
     - code_id: quantum_concatenated
       detail: 'Each pair of surface-code squares in a layer code are fused (or quasi-concatenated) with perpendicular surface-code squares via lattice surgery.'
     - code_id: self_correct

codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface/surface.yml

@@ -58,7 +58,7 @@ protection: |
 
 features:
   rate: |
-    Both the planar and toric codes saturate the BPT bound, which states that \(k d^2 = O(L^2)\) for codes on a 2D lattice of length \(O(L)\).
+    Both the planar and toric codes saturate the \hyperref[topic:BPT-bound]{BPT bound}, which states that \(k d^2 = O(L^2)\) for codes on a 2D lattice of length \(O(L)\).
 
   encoders:
     - 'A depth-\(L^2\) circuit that grows the code out of a small patch on an \(L\times L\) square lattice using CNOT gates (i.e., "local moves") \cite{arxiv:quant-ph/0110143,arxiv:0712.0348}.'