{
 "slug": "givens",
 "title": "Givens Rotation",
 "symbol": "G_{ij}",
 "aliases": [
  "givens"
 ],
 "notations": [
  "G(\\theta)",
  "G_{ij}(\\theta)"
 ],
 "description": "Two-level rotation that mixes the $|01\\rangle$ and $|10\\rangle$ subspace.",
 "arity": 2,
 "dimension": 2,
 "params": {
  "theta": {
   "label": "\\theta",
   "default": "1/4",
   "range": [
    0,
    2
   ]
  }
 },
 "matrix": [
  [
   1,
   0,
   0,
   0
  ],
  [
   0,
   "cos(theta)",
   "-sin(theta)",
   0
  ],
  [
   0,
   "sin(theta)",
   "cos(theta)",
   0
  ],
  [
   0,
   0,
   0,
   1
  ]
 ],
 "groups": [
  "orthogonal",
  "matchgate",
  "number-preserving"
 ],
 "properties": [],
 "url": "/gates/givens/"
}