{
 "slug": "clock",
 "title": "Clock",
 "symbol": "Z_d",
 "aliases": [
  "clock"
 ],
 "notations": [
  "Z_d",
  "\\Sigma_z",
  "\\sigma"
 ],
 "description": "Qudit generalization of Pauli-$Z$ that tags each basis state with a root-of-unity phase, $|j\\rangle \\mapsto \\omega^j |j\\rangle$.",
 "arity": 1,
 "dimension": "d",
 "matrix": [
  [
   "1",
   0,
   0
  ],
  [
   0,
   "exp(2 pi i/3)",
   0
  ],
  [
   0,
   0,
   "exp(4 pi i/3)"
  ]
 ],
 "matrix_note": "d = 3",
 "groups": [
  "diagonal",
  "number-preserving"
 ],
 "properties": [],
 "url": "/gates/clock/"
}