{
 "slug": "chrestenson",
 "title": "Chrestenson",
 "symbol": "C_d",
 "aliases": [
  "chrestenson",
  "chrestenson-transform",
  "generalized-hadamard"
 ],
 "notations": [
  "C_d",
  "\\mathcal{C}_d"
 ],
 "description": "Qudit generalization of the Hadamard gate that maps each basis state to an equal superposition with root-of-unity phases.",
 "arity": 1,
 "dimension": "d",
 "matrix": [
  [
   "1/sqrt(3)",
   "1/sqrt(3)",
   "1/sqrt(3)"
  ],
  [
   "1/sqrt(3)",
   "exp(2 pi i/3)/sqrt(3)",
   "exp(4 pi i/3)/sqrt(3)"
  ],
  [
   "1/sqrt(3)",
   "exp(4 pi i/3)/sqrt(3)",
   "exp(2 pi i/3)/sqrt(3)"
  ]
 ],
 "matrix_note": "d = 3",
 "groups": [],
 "properties": [],
 "url": "/gates/chrestenson/"
}