{
 "slug": "shift",
 "title": "Shift",
 "symbol": "X_d",
 "aliases": [
  "shift"
 ],
 "notations": [
  "X_d",
  "\\Sigma_x",
  "\\tau"
 ],
 "description": "Qudit generalization of Pauli-$X$ that cyclically increments the basis state, $|j\\rangle \\mapsto |j+1 \\bmod d\\rangle$.",
 "arity": 1,
 "dimension": "d",
 "matrix": [
  [
   0,
   0,
   1
  ],
  [
   1,
   0,
   0
  ],
  [
   0,
   1,
   0
  ]
 ],
 "matrix_note": "d = 3",
 "groups": [
  "orthogonal",
  "permutation"
 ],
 "properties": [],
 "url": "/gates/shift/"
}