{
 "slug": "mcx",
 "title": "Multi-Controlled X",
 "symbol": "\\mathrm{C}^nX",
 "aliases": [
  "mcx",
  "c3x",
  "c4x"
 ],
 "notations": [
  "\\mathrm{C}^nX",
  "\\Lambda^n(X)",
  "\\mathrm{MCX}",
  "\\mathrm{C}^3X"
 ],
 "description": "Flips the target qubit when all $n$ control qubits are in the $|1\\rangle$ state.",
 "arity": "n+1",
 "dimension": 2,
 "matrix": [
  [
   1,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0
  ],
  [
   0,
   1,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0
  ],
  [
   0,
   0,
   1,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0
  ],
  [
   0,
   0,
   0,
   1,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0
  ],
  [
   0,
   0,
   0,
   0,
   1,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0
  ],
  [
   0,
   0,
   0,
   0,
   0,
   1,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0
  ],
  [
   0,
   0,
   0,
   0,
   0,
   0,
   1,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0
  ],
  [
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   1,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0
  ],
  [
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   1,
   0,
   0,
   0,
   0,
   0,
   0,
   0
  ],
  [
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   1,
   0,
   0,
   0,
   0,
   0,
   0
  ],
  [
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   1,
   0,
   0,
   0,
   0,
   0
  ],
  [
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   1,
   0,
   0,
   0,
   0
  ],
  [
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   1,
   0,
   0,
   0
  ],
  [
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   1,
   0,
   0
  ],
  [
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   1
  ],
  [
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   1,
   0
  ]
 ],
 "matrix_note": "n = 3",
 "groups": [
  "orthogonal",
  "permutation"
 ],
 "properties": [
  "hermitian"
 ],
 "url": "/gates/mcx/"
}