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codes/quantum/qubits/stabilizer/magic/k-orthogonal/quantum_rainbow.yml

@@ -28,6 +28,8 @@ relations:
       detail: 'Hypergraph products of color codes yield quantum rainbow codes with growing distance and transversal gates in the \term{Clifford hierarchy}. In particular, utilizing this construction for quasi-hyperbolic color codes yields an \([[n,O(n),O(\log n)]]\) triorthogonal code family with magic-state yield parameter \(\gamma\to 0\) \cite{arxiv:2408.13130}.'
     - code_id: quantum_triorthogonal
       detail: 'Hypergraph products of color codes yield quantum rainbow codes with growing distance and transversal gates in the \term{Clifford hierarchy}. In particular, utilizing this construction for quasi-hyperbolic color codes \cite{arxiv:2310.16982} yields an \([[n,O(n),O(\log n)]]\) triorthogonal code family with magic-state yield parameter \(\gamma\to 0\) \cite{arxiv:2408.13130}.'
+    - code_id: hyperbolic_color
+      detail: 'Hypergraph products of color codes yield quantum rainbow codes with growing distance and transversal gates in the \term{Clifford hierarchy}. In particular, utilizing this construction for quasi-hyperbolic color codes yields an \([[n,O(n),O(\log n)]]\) triorthogonal code family with magic-state yield parameter \(\gamma\to 0\) \cite{arxiv:2408.13130}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/stabilizer/topological/color/hyperbolic_color.yml

@@ -15,15 +15,22 @@ description: |
   As opposed to there being only three types of uniform three-valent and three-colorable lattice tilings in the 2D Euclidean plane, there is an infinite number of admissible hyperbolic tilings in the 2D hyperbolic plane \cite{arxiv:1804.06382}.
   Certain double covers of hyperbolic tilings also yield admissible tilings \cite{arxiv:1301.6588}.
   Other admissible hyperbolic tilings can be obtained via a fattening procedure \cite{arxiv:cond-mat/0607736}; see also a construction based on the  more general quantum pin codes \cite{arxiv:1906.11394}.
+  See Ref. \cite{arxiv:2310.16982} for surface codes on quasi-hyperbolic manifolds.
 
 protection: |
   The use of hyperbolic surfaces allows one to circumvent bounds on code parameters (such as the \term{BPT bound}) that are valid for lattice geometries.
   Hyperbolic color codes can have high rate but tend to have small distance.
   For example, a \(\{4g,4g\}\) tiling with periodic boundary conditions (i.e., a \(g\)-torus) yields a \([[4g+8,4g,4]]\) code family \cite{arxiv:1804.06382}.
   More examples, such as the \([[160,20,8]]\) code on the 4.10.10 tiling, are provided in \cite[Sec. V.A]{arxiv:1906.11394}.
 
+  There exists a family with rate of \hyperref[topic:asymptotics]{order} \(O(1/\log n)\) and minimum distance of \hyperref[topic:asymptotics]{order} \(\Omega(\log n)\) which supports fault-tolerant non-Clifford gates \cite{arxiv:2310.16982}.
+  A construction based on the Torelli mapping yields a code with constant rate with similar gates \cite{arxiv:2310.16982}.
+
 features:
-  rate: 'In the double-cover construction \cite{arxiv:1301.6588}, an \(\{\ell,m\}\) input tiling yields a code family with an asymptotic rate of \(1 - 1/\ell - 1/m\).'
+  rate: 'In the double-cover construction \cite{arxiv:1301.6588}, an \(\{\ell,m\}\) input tiling yields a code family with an asymptotic rate of \(1 - 1/\ell - 1/m\). A construction based on the Torelli mapping yields a code with constant rate with similar gates \cite{arxiv:2310.16982}.'
+
+  fault_tolerance:
+    - 'There exists a family with rate of \hyperref[topic:asymptotics]{order} \(O(1/\log n)\) and minimum distance of \hyperref[topic:asymptotics]{order} \(\Omega(\log n)\) which supports fault-tolerant non-Clifford gates \cite{arxiv:2310.16982}. A construction based on the Torelli mapping yields a code with constant rate with similar gates \cite{arxiv:2310.16982}.'
 
 
 relations:

codes/quantum/qubits/stabilizer/topological/surface/hyperbolic/hyperbolic_surface.yml

@@ -12,6 +12,7 @@ name: 'Hyperbolic surface code'
 description: |
   An extension of the Kitaev surface code construction to hyperbolic manifolds.
   Given a cellulation of a manifold, qubits are put on \(i\)-dimensional faces, \(X\)-type stabilizers are associated with \((i-1)\)-faces, while \(Z\)-type stabilizers are associated with \(i+1\)-faces.
+  See Ref. \cite{arxiv:2310.16982} for surface codes on quasi-hyperbolic manifolds.
 
 protection: 'Constructions (see code children below) have yielded distances scaling favorably with the number of qubits. The use of hyperbolic surfaces allows one to circumvent bounds on code parameters (such as the \term{BPT bound}) that are valid for lattice geometries.'