{
 "slug": "grover-diffuser",
 "title": "Grover Diffuser",
 "symbol": "U_s",
 "aliases": [
  "grover-diffuser",
  "diffuser"
 ],
 "notations": [
  "U_s",
  "2|s\\rangle\\langle s| - I",
  "\\mathrm{D}"
 ],
 "description": "Reflection about the uniform superposition, the \"inversion about the mean\" step of Grover's algorithm.",
 "arity": "n",
 "dimension": 2,
 "matrix": [
  [
   "-1/2",
   "1/2",
   "1/2",
   "1/2"
  ],
  [
   "1/2",
   "-1/2",
   "1/2",
   "1/2"
  ],
  [
   "1/2",
   "1/2",
   "-1/2",
   "1/2"
  ],
  [
   "1/2",
   "1/2",
   "1/2",
   "-1/2"
  ]
 ],
 "matrix_note": "n = 2",
 "groups": [
  "orthogonal"
 ],
 "properties": [
  "hermitian"
 ],
 "url": "/gates/grover-diffuser/"
}