{
 "slug": "controlled-shift",
 "title": "Controlled Shift (SUM)",
 "symbol": "\\mathrm{SUM}_d",
 "aliases": [
  "sum",
  "cadd",
  "qudit-cx",
  "controlled-shift"
 ],
 "notations": [
  "\\mathrm{C}X_d",
  "\\mathrm{ADD}_d",
  "\\mathrm{SUM}_d"
 ],
 "description": "Qudit-controlled shift that adds the control value to the target modulo $d$.",
 "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,
   0,
   0,
   1,
   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,
   0,
   0,
   1,
   0
  ],
  [
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   1
  ],
  [
   0,
   0,
   0,
   0,
   0,
   0,
   1,
   0,
   0
  ]
 ],
 "matrix_note": "d = 3",
 "groups": [
  "orthogonal",
  "permutation"
 ],
 "properties": [],
 "url": "/gates/controlled-shift/"
}