{
  "schema": "wai.quantum.exercise/1",
  "id": "bit-flip-code",
  "translations": { "zh-CN": "machine-assisted: to be reviewed by a fluent reader before it is advertised" },
  "title": { "en": "Three copies against one flip", "zh-CN": "用三份副本抵御一次翻转" },
  "task": {
    "en": "q[0] holds |1⟩. Encode it into three qubits, let the error flip the qubit q[err] (the check tries err = 0, 1 and 2), then decode and correct so that q[0] reads 1 in every case. Use no x besides the two the program has.",
    "zh-CN": "q[0] 存有 |1⟩。把它编码到三个量子比特中，让错误翻转量子比特 q[err]（检查会依次尝试 err = 0、1 和 2），然后解码并纠正，使 q[0] 在每种情况下都读出 1。除了程序中已有的两个 x，不要再使用 x。"
  },
  "starter": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "input uint err;",
    "qubit[3] q;",
    "bit[1] c;",
    "// the state to protect",
    "x q[0];",
    "// encode: your gates here",
    "// the error, on a qubit the check chooses",
    "x q[err];",
    "// decode and correct: your gates here",
    "c[0] = measure q[0];"
  ],
  "cases": [
    { "inputs": { "err": 0 }, "name": { "en": "a flip of q[0]", "zh-CN": "q[0] 被翻转" } },
    { "inputs": { "err": 1 }, "name": { "en": "a flip of q[1]", "zh-CN": "q[1] 被翻转" } },
    { "inputs": { "err": 2 }, "name": { "en": "a flip of q[2]", "zh-CN": "q[2] 被翻转" } }
  ],
  "intent": { "distribution": { "1": 1.0 } },
  "constraints": { "allow": ["x", "cx", "ccx"], "counts": { "x": { "max": 2 } } },
  "hints": {
    "en": [
      "Encode with two controlled-NOTs from q[0]: |1⟩ becomes |111⟩, and one flip leaves two copies right.",
      "Decoding with the same two controlled-NOTs leaves q[1] and q[2] saying whether each disagrees with q[0].",
      "q[0] is wrong exactly when both other qubits disagree with it. Which gate flips a qubit when two others are both 1?"
    ],
    "zh-CN": [
      "用两个以 q[0] 为控制的受控非门编码：|1⟩ 变成 |111⟩，一次翻转之后仍有两份副本是对的。",
      "用同样的两个受控非门解码后，q[1] 和 q[2] 分别表示它是否与 q[0] 不一致。",
      "恰好当另外两个量子比特都与 q[0] 不一致时，q[0] 才是错的。哪个门会在另外两个量子比特都为 1 时翻转一个量子比特？"
    ]
  },
  "reference": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "input uint err;",
    "qubit[3] q;",
    "bit[1] c;",
    "x q[0];",
    "cx q[0], q[1];",
    "cx q[0], q[2];",
    "x q[err];",
    "cx q[0], q[1];",
    "cx q[0], q[2];",
    "ccx q[2], q[1], q[0];",
    "c[0] = measure q[0];"
  ],
  "wrong": [
    {
      "fails": "intent",
      "note": "without correction a flip of q[0] is read as 0",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "input uint err;", "qubit[3] q;", "bit[1] c;", "x q[0];", "cx q[0], q[1];", "cx q[0], q[2];", "x q[err];", "cx q[0], q[1];", "cx q[0], q[2];", "c[0] = measure q[0];"]
    },
    {
      "fails": "intent",
      "note": "correcting with one copy fixes some flips and makes others",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "input uint err;", "qubit[3] q;", "bit[1] c;", "x q[0];", "cx q[0], q[1];", "cx q[0], q[2];", "x q[err];", "cx q[0], q[1];", "cx q[0], q[2];", "cx q[1], q[0];", "c[0] = measure q[0];"]
    }
  ]
}