{
 "slug": "rot",
 "title": "Arbitrary Rotation",
 "symbol": "R_{\\mathbf{n}}",
 "aliases": [
  "rot"
 ],
 "notations": [
  "\\mathrm{Rot}(\\vec{n}, \\theta)",
  "R_{\\vec{n}}(\\theta)"
 ],
 "description": "Rotation by angle $\\theta$ about the Bloch-sphere axis $\\vec{n}$.",
 "arity": 1,
 "dimension": 2,
 "params": {
  "theta": {
   "label": "\\theta",
   "default": "1/2",
   "range": [
    0,
    2
   ]
  },
  "alpha": {
   "label": "\\alpha",
   "default": "1/4",
   "range": [
    0,
    2
   ]
  },
  "beta": {
   "label": "\\beta",
   "default": "acos(1/sqrt(3))/pi",
   "range": [
    0,
    1
   ]
  }
 },
 "matrix": [
  [
   "cos(theta/2) - i sin(theta/2) cos(beta)",
   "-i sin(theta/2) sin(beta) exp(-i alpha)"
  ],
  [
   "-i sin(theta/2) sin(beta) exp(i alpha)",
   "cos(theta/2) + i sin(theta/2) cos(beta)"
  ]
 ],
 "groups": [],
 "properties": [],
 "url": "/gates/rot/"
}