{
 "slug": "toffoli",
 "title": "Toffoli",
 "symbol": "\\mathrm{CC}X",
 "aliases": [
  "toffoli",
  "ccx"
 ],
 "notations": [
  "\\mathrm{CCX}",
  "\\mathrm{CCNOT}",
  "\\mathrm{TOFF}",
  "C^2X",
  "\\Lambda^2(X)",
  "\\text{Toffoli}"
 ],
 "description": "Controlled-controlled-NOT gate that flips a target qubit when both controls are $|1\\rangle$.",
 "arity": 3,
 "dimension": 2,
 "matrix": [
  [
   1,
   0,
   0,
   0,
   0,
   0,
   0,
   0
  ],
  [
   0,
   1,
   0,
   0,
   0,
   0,
   0,
   0
  ],
  [
   0,
   0,
   1,
   0,
   0,
   0,
   0,
   0
  ],
  [
   0,
   0,
   0,
   1,
   0,
   0,
   0,
   0
  ],
  [
   0,
   0,
   0,
   0,
   1,
   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
  ]
 ],
 "groups": [
  "orthogonal",
  "permutation"
 ],
 "properties": [
  "hermitian"
 ],
 "url": "/gates/toffoli/"
}