{
  "schema": "wai.quantum.exercise/1",
  "id": "bernstein-vazirani",
  "translations": { "zh-CN": "machine-assisted: to be reviewed by a fluent reader before it is advertised" },
  "title": { "en": "A hidden string, in one query", "zh-CN": "一次查询找出隐藏的串" },
  "task": {
    "en": "The oracle computes f(x) = s · x (mod 2) into q[3] for a hidden three-bit string s. Write the Bernstein–Vazirani circuit around it so that the measured inputs read s every time. Keep the oracle's cx gates as they are.",
    "zh-CN": "预言机为一个隐藏的三比特串 s 把 f(x) = s · x (mod 2) 计算到 q[3] 中。在它周围写出 Bernstein–Vazirani 线路，使测得的输入每次都读出 s。保持预言机的 cx 门不变。"
  },
  "starter": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "qubit[4] q;",
    "bit[3] c;",
    "// before the oracle: your gates here",
    "// the oracle: f(x) = s . x, into q[3]",
    "cx q[0], q[3];",
    "cx q[2], q[3];",
    "// after the oracle: your gates here",
    "c[0] = measure q[0];",
    "c[1] = measure q[1];",
    "c[2] = measure q[2];"
  ],
  "intent": { "distribution": { "101": 1.0 } },
  "constraints": { "allow": ["h", "x", "cx"], "counts": { "cx": { "min": 2, "max": 2 }, "x": { "max": 1 } } },
  "hints": {
    "en": [
      "The circuit has the same shape as Deutsch–Jozsa's, with one more input.",
      "With every input in superposition and the target in |−⟩, the oracle leaves the sign (−1)^(s·x) on |x⟩; Hadamards turn that pattern of signs into |s⟩."
    ],
    "zh-CN": [
      "这条线路与 Deutsch–Jozsa 的形状相同，只是多一个输入。",
      "当每个输入都处于叠加、目标比特处于 |−⟩ 时，预言机在 |x⟩ 上留下符号 (−1)^(s·x)；Hadamard 门把这种符号模式变成 |s⟩。"
    ]
  },
  "reference": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "qubit[4] q;",
    "bit[3] c;",
    "x q[3];",
    "h q;",
    "cx q[0], q[3];",
    "cx q[2], q[3];",
    "h q[0];",
    "h q[1];",
    "h q[2];",
    "c[0] = measure q[0];",
    "c[1] = measure q[1];",
    "c[2] = measure q[2];"
  ],
  "wrong": [
    {
      "fails": "intent",
      "note": "querying one basis input reads one bit of s at most",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "qubit[4] q;", "bit[3] c;", "x q[0];", "cx q[0], q[3];", "cx q[2], q[3];", "c[0] = measure q[0];", "c[1] = measure q[1];", "c[2] = measure q[2];"]
    }
  ]
}