{
  "schema": "wai.quantum.exercise/1",
  "id": "folding",
  "translations": { "zh-CN": "machine-assisted: to be reviewed by a fluent reader before it is advertised" },
  "title": { "en": "Amplifying noise on purpose", "zh-CN": "有意放大噪声" },
  "task": {
    "en": "Fold the Bell pair's two-qubit gate for zero-noise extrapolation: replace its one cx by three, so that the program is still the same circuit but carries three times the two-qubit noise.",
    "zh-CN": "为零噪声外推折叠 Bell 对中的双比特门：把那一个 cx 换成三个，使程序仍是同一条线路，却承受三倍的双比特噪声。"
  },
  "starter": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "qubit[2] q;",
    "bit[2] c;",
    "h q[0];",
    "cx q[0], q[1];",
    "c = measure q;"
  ],
  "intent": {
    "equivalent": "OPENQASM 3.0;\ninclude \"stdgates.inc\";\nqubit[2] q;\nbit[2] c;\nh q[0];\ncx q[0], q[1];\nc = measure q;\n"
  },
  "constraints": { "allow": ["h", "cx"], "counts": { "cx": { "min": 3, "max": 3 }, "h": { "max": 1 } } },
  "hints": {
    "en": [
      "A gate followed by its inverse does nothing. What is the inverse of cx?",
      "G becomes G G⁻¹ G: the same circuit, with three times the gate's noise."
    ],
    "zh-CN": [
      "一个门后面跟着它的逆，就什么也不做。cx 的逆是什么？",
      "G 变成 G G⁻¹ G：线路不变，而这个门的噪声变为三倍。"
    ]
  },
  "reference": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "qubit[2] q;",
    "bit[2] c;",
    "h q[0];",
    "cx q[0], q[1];",
    "cx q[0], q[1];",
    "cx q[0], q[1];",
    "c = measure q;"
  ],
  "wrong": [
    {
      "fails": "constraint",
      "note": "two copies cancel each other and leave no entangling gate",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "qubit[2] q;", "bit[2] c;", "h q[0];", "cx q[0], q[1];", "cx q[0], q[1];", "c = measure q;"]
    },
    {
      "fails": "intent",
      "note": "three cx with the direction of one reversed is a different circuit",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "qubit[2] q;", "bit[2] c;", "h q[0];", "cx q[0], q[1];", "cx q[1], q[0];", "cx q[0], q[1];", "c = measure q;"]
    }
  ]
}