{
  "schema": "wai.quantum.exercise/1",
  "id": "qft",
  "translations": { "zh-CN": "machine-assisted: to be reviewed by a fluent reader before it is advertised" },
  "title": { "en": "The quantum Fourier transform, and back", "zh-CN": "量子傅里叶变换，以及它的逆" },
  "task": {
    "en": "The program applies the three-qubit quantum Fourier transform. After it, write the inverse transform, so that the whole program is the same circuit as doing nothing. Keep the transform's gates as they are.",
    "zh-CN": "这个程序作用了三量子比特的量子傅里叶变换。在它之后写出逆变换，使整个程序与什么也不做是同一条线路。保持变换本身的门不变。"
  },
  "starter": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "qubit[3] q;",
    "// the quantum Fourier transform",
    "h q[0];",
    "cp(pi/2) q[1], q[0];",
    "cp(pi/4) q[2], q[0];",
    "h q[1];",
    "cp(pi/2) q[2], q[1];",
    "h q[2];",
    "swap q[0], q[2];",
    "// its inverse: your gates here"
  ],
  "intent": { "equivalent": "OPENQASM 3.0;\ninclude \"stdgates.inc\";\nqubit[3] q;\n" },
  "constraints": { "allow": ["h", "cp", "swap"], "counts": { "h": { "min": 6, "max": 6 }, "cp": { "min": 6, "max": 6 }, "swap": { "min": 2, "max": 2 } } },
  "hints": {
    "en": [
      "The inverse of a sequence of gates is the inverses of the gates, in the reverse order.",
      "h and swap are their own inverses. The inverse of cp(θ) is cp(−θ) on the same qubits."
    ],
    "zh-CN": [
      "一串门的逆，就是把每个门换成它的逆，再把顺序倒过来。",
      "h 和 swap 都是自己的逆。cp(θ) 的逆是作用在同样量子比特上的 cp(−θ)。"
    ]
  },
  "reference": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "qubit[3] q;",
    "h q[0];",
    "cp(pi/2) q[1], q[0];",
    "cp(pi/4) q[2], q[0];",
    "h q[1];",
    "cp(pi/2) q[2], q[1];",
    "h q[2];",
    "swap q[0], q[2];",
    "swap q[0], q[2];",
    "h q[2];",
    "cp(-pi/2) q[2], q[1];",
    "h q[1];",
    "cp(-pi/4) q[2], q[0];",
    "cp(-pi/2) q[1], q[0];",
    "h q[0];"
  ],
  "wrong": [
    {
      "fails": "intent",
      "note": "the gates reversed but the angles not negated",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "qubit[3] q;", "h q[0];", "cp(pi/2) q[1], q[0];", "cp(pi/4) q[2], q[0];", "h q[1];", "cp(pi/2) q[2], q[1];", "h q[2];", "swap q[0], q[2];", "swap q[0], q[2];", "h q[2];", "cp(pi/2) q[2], q[1];", "h q[1];", "cp(pi/4) q[2], q[0];", "cp(pi/2) q[1], q[0];", "h q[0];"]
    },
    {
      "fails": "constraint",
      "note": "deleting the transform does nothing too, but the exercise keeps its gates",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "qubit[3] q;"]
    }
  ]
}