{
  "schema": "wai.quantum.exercise/1",
  "id": "deutsch-jozsa",
  "translations": { "zh-CN": "machine-assisted: to be reviewed by a fluent reader before it is advertised" },
  "title": { "en": "Constant or balanced, in one query", "zh-CN": "常数还是平衡，一次查询见分晓" },
  "task": {
    "en": "The oracle computes f(x₀, x₁) = x₀ ⊕ x₁ into q[2]: a balanced function. Around it, write the Deutsch–Jozsa circuit so that the measured inputs read 11 every time. Keep the oracle's two cx gates as they are.",
    "zh-CN": "预言机（oracle）把 f(x₀, x₁) = x₀ ⊕ x₁ 计算到 q[2] 中：这是一个平衡函数。在它周围写出 Deutsch–Jozsa 线路，使测得的输入每次都读出 11。保持预言机的两个 cx 门不变。"
  },
  "starter": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "qubit[3] q;",
    "bit[2] c;",
    "// before the oracle: your gates here",
    "// the oracle: f(x) = x0 xor x1, into q[2]",
    "cx q[0], q[2];",
    "cx q[1], q[2];",
    "// after the oracle: your gates here",
    "c[0] = measure q[0];",
    "c[1] = measure q[1];"
  ],
  "intent": { "distribution": { "11": 1.0 } },
  "constraints": { "allow": ["h", "x", "cx"], "counts": { "cx": { "min": 2, "max": 2 }, "x": { "max": 1 } } },
  "hints": {
    "en": [
      "Put the inputs in superposition, so that the oracle is asked about every input at once.",
      "Prepare q[2] in |−⟩ before the oracle: then f(x) comes back as a sign on |x⟩, by phase kickback.",
      "After the oracle, interfere the inputs again. A constant function would bring them back to 00."
    ],
    "zh-CN": [
      "让输入处于叠加，这样一次就同时向预言机询问了所有输入。",
      "在预言机之前把 q[2] 制备到 |−⟩：这样 f(x) 会通过相位反冲，以 |x⟩ 上的符号返回。",
      "预言机之后，再让输入发生一次干涉。如果函数是常数，输入会回到 00。"
    ]
  },
  "reference": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "qubit[3] q;",
    "bit[2] c;",
    "x q[2];",
    "h q[0];",
    "h q[1];",
    "h q[2];",
    "cx q[0], q[2];",
    "cx q[1], q[2];",
    "h q[0];",
    "h q[1];",
    "c[0] = measure q[0];",
    "c[1] = measure q[1];"
  ],
  "wrong": [
    {
      "fails": "intent",
      "note": "with q[2] left in |0⟩ the answer never comes back as a phase",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "qubit[3] q;", "bit[2] c;", "h q[0];", "h q[1];", "cx q[0], q[2];", "cx q[1], q[2];", "h q[0];", "h q[1];", "c[0] = measure q[0];", "c[1] = measure q[1];"]
    },
    {
      "fails": "constraint",
      "note": "an oracle with one cx removed is a different function",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "qubit[3] q;", "bit[2] c;", "x q[2];", "h q[0];", "h q[1];", "h q[2];", "cx q[0], q[2];", "h q[0];", "h q[1];", "c[0] = measure q[0];", "c[1] = measure q[1];"]
    }
  ]
}