{
  "schema": "wai.quantum.exercise/1",
  "id": "estimate",
  "translations": { "zh-CN": "machine-assisted: to be reviewed by a fluent reader before it is advertised" },
  "title": { "en": "What a fault-tolerant machine would need", "zh-CN": "容错机器需要什么" },
  "task": {
    "en": "This program computes a carry into q[2], copies it into q[3], and uncomputes it: the resource estimate counts two Toffolis. Rewrite it as the same circuit, on the same four qubits, so that the resource estimate counts at most one Toffoli.",
    "zh-CN": "这个程序把一个进位计算到 q[2]，复制到 q[3]，再把它反计算掉：资源估算计入两个 Toffoli 门。把它改写成同一条线路（仍是这四个量子比特），使资源估算至多只计入一个 Toffoli 门。"
  },
  "starter": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "qubit[4] q;",
    "// compute the carry a AND b into q[2]",
    "ccx q[0], q[1], q[2];",
    "// copy it into q[3]",
    "cx q[2], q[3];",
    "// uncompute the carry",
    "ccx q[0], q[1], q[2];"
  ],
  "intent": {
    "equivalent": "OPENQASM 3.0;\ninclude \"stdgates.inc\";\nqubit[4] q;\nccx q[0], q[1], q[2];\ncx q[2], q[3];\nccx q[0], q[1], q[2];\n"
  },
  "constraints": { "estimate": { "toffolis": { "max": 1 } } },
  "hints": {
    "en": [
      "Follow one basis input through the three gates: what does q[3] end with, in terms of q[0], q[1] and q[2]'s starting value?",
      "q[3] ends as q[3] ⊕ (q[0] AND q[1]) ⊕ q[2], and q[2] ends as it began. One Toffoli and one controlled-NOT write that."
    ],
    "zh-CN": [
      "让一个基态输入依次经过这三个门：用 q[0]、q[1] 和 q[2] 的初始值来表示，q[3] 最后是什么？",
      "q[3] 最后等于 q[3] ⊕ (q[0] AND q[1]) ⊕ q[2]，而 q[2] 回到初始值。一个 Toffoli 门加一个受控非门就能写出它。"
    ]
  },
  "reference": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "qubit[4] q;",
    "ccx q[0], q[1], q[3];",
    "cx q[2], q[3];"
  ],
  "wrong": [
    {
      "fails": "intent",
      "note": "dropping the copy of q[2] changes what happens when q[2] starts at 1",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "qubit[4] q;", "ccx q[0], q[1], q[3];"]
    },
    {
      "fails": "constraint",
      "note": "the same circuit, still at two Toffolis",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "qubit[4] q;", "ccx q[0], q[1], q[2];", "cx q[2], q[3];", "ccx q[0], q[1], q[2];"]
    }
  ]
}