{
  "schema": "wai.quantum.exercise/1",
  "id": "grover",
  "translations": { "zh-CN": "machine-assisted: to be reviewed by a fluent reader before it is advertised" },
  "title": { "en": "Searching by amplitude", "zh-CN": "靠振幅来搜索" },
  "task": {
    "en": "Two qubits in uniform superposition, and an oracle that marks 11 with a minus sign. Add the diffusion step so that one round of Grover's search finds 11 every time. No two gates of your program may cancel.",
    "zh-CN": "两个处于均匀叠加的量子比特，以及一个用负号标记 11 的预言机。加上扩散（diffusion）步骤，使一轮 Grover 搜索每次都找到 11。程序中不得有相互抵消的门。"
  },
  "starter": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "qubit[2] q;",
    "bit[2] c;",
    "h q;",
    "// the oracle: a minus sign on 11",
    "cz q[0], q[1];",
    "// the diffusion: your gates here",
    "c = measure q;"
  ],
  "intent": { "distribution": { "11": 1.0 } },
  "constraints": { "allow": ["h", "x", "z", "cz"], "counts": { "cz": { "min": 2, "max": 2 } }, "no_smells": ["cancels", "merges", "does_nothing"] },
  "hints": {
    "en": [
      "The oracle's sign is invisible to a measurement: the outcomes are still uniform. The diffusion turns it into amplitude.",
      "The diffusion reflects every amplitude about their average. Built from gates, it is a sign on 00 between two layers of Hadamards.",
      "To put a sign on 00 with cz, which signs 11, flip both qubits before and after it."
    ],
    "zh-CN": [
      "预言机加上的符号在测量中是看不见的：结果仍然是均匀的。扩散步骤把它变成振幅上的差别。",
      "扩散步骤把每个振幅关于它们的平均值作反射。用门来搭建时，它就是夹在两层 Hadamard 门之间、加在 00 上的一个符号。",
      "cz 给 11 加符号；要用它给 00 加符号，就在它前后把两个量子比特都翻转。"
    ]
  },
  "reference": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "qubit[2] q;",
    "bit[2] c;",
    "h q;",
    "cz q[0], q[1];",
    "h q;",
    "x q;",
    "cz q[0], q[1];",
    "x q;",
    "h q;",
    "c = measure q;"
  ],
  "wrong": [
    {
      "fails": "intent",
      "note": "the oracle alone leaves the outcomes uniform",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "qubit[2] q;", "bit[2] c;", "h q;", "cz q[0], q[1];", "c = measure q;"]
    },
    {
      "fails": "constraint",
      "note": "undoing the oracle and flipping both qubits finds 11 without searching",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "qubit[2] q;", "bit[2] c;", "h q;", "cz q[0], q[1];", "cz q[0], q[1];", "h q;", "x q;", "c = measure q;"]
    }
  ]
}