polyhedron

codes/classical/spherical/polytope/polyhedron/cubeoctahedron.yml → codes/classical/spherical/polytope/3d/cubeoctahedron.yml

@@ -19,7 +19,7 @@ protection: |
 
 relations:
   parents:
-    - code_id: polytope
+    - code_id: polyhedron
     - code_id: lattice_shell
       detail: 'Cubeoctahedron codewords form the minimal shell of the \(D_3\) face-centered cubic (fcc) lattice.'
   cousins:

codes/classical/spherical/polytope/polyhedron/dodecahedron.yml → codes/classical/spherical/polytope/3d/dodecahedron.yml

@@ -15,7 +15,7 @@ description: |
 
 relations:
   parents:
-    - code_id: polytope
+    - code_id: polyhedron
     - code_id: spherical_design
       detail: 'The dodecahedron code forms a spherical 5-design \cite{arxiv:2302.11593}.'
   cousins:

codes/classical/spherical/polytope/polyhedron/icosahedron.yml → codes/classical/spherical/polytope/3d/icosahedron.yml

@@ -20,7 +20,7 @@ notes:
 
 relations:
   parents:
-    - code_id: polytope
+    - code_id: polyhedron
     - code_id: sharp_config
       detail: 'The icosahedron is a sharp configuration \cite{manual:{Andreev, Nikolay N. "An extremal property of the icosahedron." East J. Approx 2.4 (1996): 459-462.},arxiv:math/0607446}.'
     - code_id: spherical_design

codes/classical/spherical/polytope/polyhedron/pentakis_dodecahedron.yml → codes/classical/spherical/polytope/3d/pentakis_dodecahedron.yml

@@ -15,7 +15,7 @@ description: |
 
 relations:
   parents:
-    - code_id: polytope
+    - code_id: polyhedron
     - code_id: spherical_design
       detail: 'Vertices of the pentakis dodecahedron form a weighted spherical 9-design \cite{doi:10.1007/978-1-4612-5648-9_13,doi:10.1016/j.laa.2020.08.010}\cite[Exam. 2.5]{arxiv:2403.07457}.'
   cousins:

codes/classical/spherical/polytope/3d/polyhedron.yml

@@ -0,0 +1,28 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: polyhedron
+physical: spheres
+logical: reals
+
+name: 'Polyhedron code'
+
+description: |
+  A polytope code in three dimensions, i.e., a spherical code whose codewords form vertices of a polyhedron.
+
+
+relations:
+  parents:
+    - code_id: polytope
+      detail: 'Three-dimensional polytope codes are polyhedron codes.'
+
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-12-10'

codes/classical/spherical/polytope/polyhedron/snub_cube.yml → codes/classical/spherical/polytope/3d/snub_cube.yml

@@ -16,7 +16,7 @@ protection: 'Optimal configuration of 24 points in 3D space \cite[pg. 78]{preset
 
 relations:
   parents:
-    - code_id: polytope
+    - code_id: polyhedron
 
 
 # Begin Entry Meta Information

codes/classical/spherical/polytope/polyhedron/square_antiprism.yml → codes/classical/spherical/polytope/3d/square_antiprism.yml

@@ -16,7 +16,7 @@ protection: 'Optimal configuration of nine points in 3D space \cite[pg. 73]{pres
 
 relations:
   parents:
-    - code_id: polytope
+    - code_id: polyhedron
 
 
 # Begin Entry Meta Information

codes/classical/spherical/polytope/polytope.yml

@@ -10,8 +10,8 @@ logical: reals
 name: 'Polytope code'
 
 description: |
-  Spherical code whose codewords are the vertices of a polytope, i.e., a geometrical figure bounded by lines, planes, and hyperplanes \cite{preset:coxeter}.
-  Polytopes in two (three, four) real or complex dimensions are called polygons (polyhedra, polychora).
+  Spherical code whose codewords are the vertices of a polytope, i.e., a geometrical figure bounded by lines, planes, and hyperplanes in either real \cite{preset:coxeter} or complex \cite{preset:coxeterComplex} space.
+  A polytope in two (three, four) dimensions is called a polygon (polyhedron, polychoron).
 
 
 relations:
@@ -23,6 +23,7 @@ relations:
 notes:
   - 'See \href{https://polytope.miraheze.org/wiki/Main_Page}{Polytope Wiki} and \href{https://bendwavy.org/klitzing/home.htm}{webpage by R. Klitzing} for lists of polytopes.'
 
+
 # Begin Entry Meta Information
 _meta:
   # Change log - most recent first

codes/quantum/properties/hamiltonian/hamiltonian.yml

@@ -35,7 +35,8 @@ description: |
 
   Two states in the same phases can be deformed into one another by evolving, via quasi-adiabatic evolution, for a time independent of the system size \(n\) \cite[Appendix]{arxiv:1004.3835}.
   The unitary operation generated by a quasi-local Hamiltonian can be simulated by a quantum circuit, with the time of evolution determining the depth of the circuit.
-  Approximating such constant-time evolution with constant error using a quantum circuit can be done in constant depth \cite{doi:10.1126/science.273.5278.1073}.
+  Approximating such constant-time evolution with constant error using a quantum circuit can be done in constant depth for finite system size \cite{doi:10.1126/science.273.5278.1073}.
+  For infinite system size, Haah proved that every bounded local Hamiltonian evolution is a limit of a sequence of locality-preserving automorphisms (a.k.a. quantum cellular automata, or QCAs) \cite[Thm. A.17]{arxiv:2211.02086}.
 
   States in certain phases (e.g., \hyperref[code:topological]{topological phases}) remain in said phases even after evolving for longer times (e.g., times that are logarithmic in \(n\)).
   This means that circuits of non-constant depth may leave a state in the same phase, making the phase classification problem quantum computationally hard \cite{arxiv:2407.07754}.

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

@@ -78,6 +78,7 @@ features:
 
   general_gates:
     - 'Fault-tolerant logical measurements that generalize a previous construction \cite{arxiv:2110.10794} and that require an \hyperref[topic:asymptotics]{order} \(O(d/\beta)\) ancilla qubits, where \(\beta\) is the Cheeger constant of the Tanner subgraph supporting the logical operator to be measured.'
+    - 'Repetition-code adapter for logical Pauli measurements and logical CNOT gates via Dehn twists \cite{arxiv:2410.03628}.'
 
   decoders:
     - 'Iterative error estimation based on the MIN-SUM and SUM-PRODUCT algorithms \cite{arxiv:quant-ph/0502086}.'

codes/quantum/qubits/stabilizer/topological/color/3d_color/cubic_honeycomb_color.yml

@@ -13,6 +13,9 @@ introduced: '\cite{arxiv:cond-mat/0607736}'
 description: |
   3D color code defined on a four-colorable bitruncated cubic honeycomb uniform tiling.
 
+features:
+  transversal_gates: 'A code family on a truncated cube with particular boundary conditions admits a transversal control-\(S\) gate via physical \(T\) and \(T^{\dagger}\) gates \cite{arxiv:2411.15035}.'
+
 
 relations:
   parents: