{
  "schema": "wai.quantum.exercise/1",
  "id": "t-count",
  "translations": { "zh-CN": "machine-assisted: to be reviewed by a fluent reader before it is advertised" },
  "title": { "en": "Counting what costs", "zh-CN": "统计真正的代价" },
  "task": {
    "en": "This program uses eight T and T† gates. Rewrite it as the same circuit with no T or T† gate at all.",
    "zh-CN": "这个程序用了八个 T 和 T† 门。把它改写成同一条线路，而且完全不用 T 或 T† 门。"
  },
  "starter": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "qubit[2] q;",
    "t q[0];",
    "t q[0];",
    "cx q[0], q[1];",
    "t q[1];",
    "tdg q[1];",
    "t q[1];",
    "t q[1];",
    "t q[1];",
    "t q[1];"
  ],
  "intent": {
    "equivalent": "OPENQASM 3.0;\ninclude \"stdgates.inc\";\nqubit[2] q;\nt q[0];\nt q[0];\ncx q[0], q[1];\nt q[1];\ntdg q[1];\nt q[1];\nt q[1];\nt q[1];\nt q[1];\n"
  },
  "constraints": { "t_count": { "max": 0 } },
  "hints": {
    "en": [
      "T is a quarter turn of S: T·T = S, and S·S = Z. A T next to a T† does nothing.",
      "The rewrite lens does it one checked step at a time: `wai-quantum rewrite simplify`, or **Rewrites** in the Studio."
    ],
    "zh-CN": [
      "T 是 S 的一半：T·T = S，而 S·S = Z。T 与 T† 相邻时什么也不做。",
      "重写透镜（rewrite lens）会一次一步地完成它，每一步都经过检查：`wai-quantum rewrite simplify`，或 Studio 中的 **Rewrites**。"
    ]
  },
  "reference": [
    "OPENQASM 3.0;",
    "include \"stdgates.inc\";",
    "qubit[2] q;",
    "s q[0];",
    "cx q[0], q[1];",
    "z q[1];"
  ],
  "wrong": [
    {
      "fails": "intent",
      "note": "S and Z swapped: a different circuit",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "qubit[2] q;", "z q[0];", "cx q[0], q[1];", "s q[1];"]
    },
    {
      "fails": "constraint",
      "note": "merged, but T gates remain",
      "qasm": ["OPENQASM 3.0;", "include \"stdgates.inc\";", "qubit[2] q;", "s q[0];", "cx q[0], q[1];", "t q[1];", "t q[1];", "s q[1];"]
    }
  ]
}