{
  "schema": "wai.quantum.exercise/1",
  "id": "rotation",
  "translations": { "zh-CN": "machine-assisted: to be reviewed by a fluent reader before it is advertised" },
  "title": { "en": "Probabilities other than one half", "zh-CN": "不是二分之一的概率" },
  "task": {
    "en": "One qubit. Make its measurement give 1 with probability exactly 1/4, using one rotation ry(θ).",
    "zh-CN": "一个量子比特。只用一个旋转门 ry(θ)，让测量以恰好 1/4 的概率给出 1。"
  },
  "starter": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "qubit[1] q;",
    "bit[1] c;",
    "ry(pi/2) q[0];",
    "c = measure q;"
  ],
  "intent": { "distribution": { "0": 0.75, "1": 0.25 } },
  "constraints": { "allow": ["ry"], "counts": { "ry": { "min": 1, "max": 1 } } },
  "hints": {
    "en": [
      "After ry(θ) on |0⟩, the probability of 1 is sin²(θ/2).",
      "Which angle has a sine of one half?"
    ],
    "zh-CN": [
      "对 |0⟩ 作用 ry(θ) 之后，得到 1 的概率是 sin²(θ/2)。",
      "哪个角的正弦等于二分之一？"
    ]
  },
  "reference": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "qubit[1] q;",
    "bit[1] c;",
    "ry(pi/3) q[0];",
    "c = measure q;"
  ],
  "wrong": [
    {
      "fails": "intent",
      "note": "θ = π/4 gives sin²(π/8), about 0.146",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "qubit[1] q;", "bit[1] c;", "ry(pi/4) q[0];", "c = measure q;"]
    },
    {
      "fails": "constraint",
      "note": "two rotations where the exercise asks for one",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "qubit[1] q;", "bit[1] c;", "ry(pi/6) q[0];", "ry(pi/6) q[0];", "c = measure q;"]
    }
  ]
}