{
  "schema": "wai.quantum.exercise/1",
  "id": "kickback",
  "translations": { "zh-CN": "machine-assisted: to be reviewed by a fluent reader before it is advertised" },
  "title": { "en": "Phase kickback", "zh-CN": "相位反冲" },
  "task": {
    "en": "q[1] starts in |−⟩, prepared for you. Make q[0] end in |1⟩ with q[1] still in |−⟩, using h and cx, and no x on q[0]. The check compares the whole state.",
    "zh-CN": "q[1] 从已为你制备好的 |−⟩ 开始。只用 h 和 cx（不要对 q[0] 作用 x），让 q[0] 最终处于 |1⟩，同时 q[1] 仍处于 |−⟩。检查比较的是整个状态。"
  },
  "starter": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "qubit[2] q;",
    "bit[1] c;",
    "// q[1] in |−⟩",
    "x q[1];",
    "h q[1];",
    "// your gates here",
    "c[0] = measure q[0];"
  ],
  "intent": {
    "prepares": "OPENQASM 3.0;\ninclude \"stdgates.inc\";\nqubit[2] q;\nbit[1] c;\nx q[0];\nx q[1];\nh q[1];\nc[0] = measure q[0];\n"
  },
  "constraints": { "allow": ["h", "x", "cx"], "counts": { "x": { "max": 1 }, "cx": { "min": 1 } } },
  "hints": {
    "en": [
      "On a target in |−⟩, a controlled-NOT does not change the target: it puts a minus sign on the control's |1⟩ instead.",
      "A sign on |1⟩ is invisible until the control goes through a gate that mixes |0⟩ and |1⟩, before and after."
    ],
    "zh-CN": [
      "当目标比特处于 |−⟩ 时，受控非门不会改变目标比特，而是在控制比特的 |1⟩ 上加一个负号。",
      "|1⟩ 上的符号是看不见的，除非控制比特在此前和此后都经过一个把 |0⟩ 和 |1⟩ 混合起来的门。"
    ]
  },
  "reference": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "qubit[2] q;",
    "bit[1] c;",
    "x q[1];",
    "h q[1];",
    "h q[0];",
    "cx q[0], q[1];",
    "h q[0];",
    "c[0] = measure q[0];"
  ],
  "wrong": [
    {
      "fails": "intent",
      "note": "without the second Hadamard the kicked phase never becomes an outcome",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "qubit[2] q;", "bit[1] c;", "x q[1];", "h q[1];", "h q[0];", "cx q[0], q[1];", "c[0] = measure q[0];"]
    },
    {
      "fails": "constraint",
      "note": "flipping q[0] directly uses a second x",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "qubit[2] q;", "bit[1] c;", "x q[1];", "h q[1];", "x q[0];", "c[0] = measure q[0];"]
    }
  ]
}