NODE 734 — TERMINAL RELAY

{
  "type": "quantum",
  "gates": [
    "T",
    "Y",
    "X",
    "H",
    "Y",
    "X",
    "H",
    "X"
  ],
  "final_states": [
    [
      [
        0.1205366803,
        0.0
      ],
      [
        0.7019511766,
        0.7019511766
      ]
    ],
    [
      [
        -0.9927088741,
        0.0
      ],
      [
        0.085232304,
        0.085232304
      ]
    ],
    [
      [
        0.5680647467,
        0.0
      ],
      [
        0.5819374724,
        0.5819374724
      ]
    ],
    [
      [
        -0.8854560257,
        0.0
      ],
      [
        0.3286089063,
        0.3286089063
      ]
    ],
    [
      [
        0.464723172,
        0.0
      ],
      [
        0.6261119602,
        0.6261119602
      ]
    ],
    [
      [
        0.8229838659,
        0.0
      ],
      [
        0.4016824346,
        0.4016824346
      ]
    ],
    [
      [
        -1.0,
        0.0
      ],
      [
        0.0,
        0.0
      ]
    ],
    [
      [
        -0.9927088741,
        0.0
      ],
      [
        0.085232304,
        0.085232304
      ]
    ],
    [
      [
        -0.2393156643,
        0.0
      ],
      [
        0.6865595432,
        0.6865595432
      ]
    ],
    [
      [
        -0.8854560257,
        0.0
      ],
      [
        0.3286089063,
        0.3286089063
      ]
    ]
  ],
  "note": "Each final state is a 2-component complex qubit state. Apply the inverse gates in REVERSE order to recover the initial state. For each recovered initial state (which should be purely real), recover the angle via theta = 2 * atan2(amp1, amp0), then map to letter via round(theta * 26 / (2pi)) -> chr(65 + idx). Gate inverses: H=H, X=X, Y=Y, Z=Z, S^-1=[[1,0],[0,-i]], T^-1=[[1,0],[0,e^-i*pi/4]]",
  "hint": "Quantum gate cipher \u2014 difficulty 6. Gate sequence (8 gates): T -> Y -> X -> H -> Y -> X -> H -> X. Word length: 10 characters. Apply inverse gates in reverse order to each final state, recover the angle from the |0> amplitude, map to A-Z.",
  "answer_format": "lowercase decoded message"
}