{
 "slug": "controlled-clock",
 "title": "Controlled Clock",
 "symbol": "\\mathrm{C}Z_d",
 "aliases": [
  "controlled-clock",
  "qudit-cz",
  "czd",
  "controlled-zd"
 ],
 "notations": [
  "\\mathrm{C}Z_d",
  "\\mathrm{CP}_d",
  "\\Lambda(Z_d)"
 ],
 "description": "Qudit generalization of controlled-$Z$ that applies the phase $\\omega^{ct}$ to $|c,t\\rangle$.",
 "arity": 2,
 "dimension": "d",
 "matrix": [
  [
   "1",
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0
  ],
  [
   0,
   "1",
   0,
   0,
   0,
   0,
   0,
   0,
   0
  ],
  [
   0,
   0,
   "1",
   0,
   0,
   0,
   0,
   0,
   0
  ],
  [
   0,
   0,
   0,
   "1",
   0,
   0,
   0,
   0,
   0
  ],
  [
   0,
   0,
   0,
   0,
   "exp(2 pi i/3)",
   0,
   0,
   0,
   0
  ],
  [
   0,
   0,
   0,
   0,
   0,
   "exp(4 pi i/3)",
   0,
   0,
   0
  ],
  [
   0,
   0,
   0,
   0,
   0,
   0,
   "1",
   0,
   0
  ],
  [
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   "exp(4 pi i/3)",
   0
  ],
  [
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   "exp(2 pi i/3)"
  ]
 ],
 "matrix_note": "d = 3",
 "groups": [
  "diagonal",
  "number-preserving"
 ],
 "properties": [],
 "url": "/gates/controlled-clock/"
}