{
  "schema": "rrc_qaoa_emc2_v1",
  "computed_at": "2026-06-21T04:32:13.556143+00:00",
  "equation": "E = mc^2",
  "qaoa_config": {
    "n_qubits": 8,
    "p_layers": 2,
    "shots": 2000,
    "optimize_maxiter": 80,
    "backend": "fallback_statevector"
  },
  "qubo": {
    "n": 8,
    "matrix": {
      "(0,0)": -1.0,
      "(1,1)": 0.5,
      "(2,2)": 0.3,
      "(3,3)": 0.8,
      "(4,4)": 2.0,
      "(5,5)": 1.5,
      "(6,6)": 1.0,
      "(7,7)": 0.7,
      "(0,1)": -0.3,
      "(0,2)": -0.2,
      "(4,5)": 0.5,
      "(4,6)": 0.5
    },
    "offset": 0.0
  },
  "ising": {
    "h": {
      "A": -0.625,
      "T": 0.175,
      "G": 0.09999999999999999,
      "C": 0.4,
      "B": 1.25,
      "S": 0.875,
      "P": 0.625,
      "Z": 0.35
    },
    "J": {
      "(A,T)": -0.075,
      "(A,G)": -0.05,
      "(B,S)": 0.125,
      "(B,P)": 0.125
    },
    "offset": 3.025
  },
  "pauli_terms": [
    {
      "pauli": "ZIIIIIII",
      "coefficient": -0.625,
      "description": "Z_A"
    },
    {
      "pauli": "IZIIIIII",
      "coefficient": 0.175,
      "description": "Z_T"
    },
    {
      "pauli": "IIZIIIII",
      "coefficient": 0.09999999999999999,
      "description": "Z_G"
    },
    {
      "pauli": "IIIZIIII",
      "coefficient": 0.4,
      "description": "Z_C"
    },
    {
      "pauli": "IIIIZIII",
      "coefficient": 1.25,
      "description": "Z_B"
    },
    {
      "pauli": "IIIIIZII",
      "coefficient": 0.875,
      "description": "Z_S"
    },
    {
      "pauli": "IIIIIIZI",
      "coefficient": 0.625,
      "description": "Z_P"
    },
    {
      "pauli": "IIIIIIIZ",
      "coefficient": 0.35,
      "description": "Z_Z"
    },
    {
      "pauli": "ZZIIIIII",
      "coefficient": -0.075,
      "description": "Z_A * Z_T"
    },
    {
      "pauli": "ZIZIIIII",
      "coefficient": -0.05,
      "description": "Z_A * Z_G"
    },
    {
      "pauli": "IIIIZZII",
      "coefficient": 0.125,
      "description": "Z_B * Z_S"
    },
    {
      "pauli": "IIIIZIZI",
      "coefficient": 0.125,
      "description": "Z_B * Z_P"
    }
  ],
  "circuit": {
    "depth": 14,
    "n_qubits": 8,
    "p_layers": 2,
    "gamma": [
      0.4410760709848923,
      0.7135455079494116
    ],
    "beta": [
      0.09445627354796624,
      0.36513477467188205
    ]
  },
  "optimization": {
    "gamma": [
      0.4410760709848923,
      0.7135455079494116
    ],
    "beta": [
      0.09445627354796624,
      0.36513477467188205
    ],
    "best_expectation": 2.868049999999997,
    "iterations": 34,
    "runtime_s": 0.7084,
    "status": "Return from COBYLA because the trust region radius reaches its lower bound."
  },
  "measurement": {
    "top_outcomes": [
      {
        "bitstring": "10000100",
        "count": 19,
        "probability": 0.0095,
        "energy": 0.5,
        "active_states": [
          "A",
          "S"
        ]
      },
      {
        "bitstring": "01000011",
        "count": 18,
        "probability": 0.009,
        "energy": 2.2,
        "active_states": [
          "T",
          "P",
          "Z"
        ]
      },
      {
        "bitstring": "00011000",
        "count": 18,
        "probability": 0.009,
        "energy": 2.8,
        "active_states": [
          "C",
          "B"
        ]
      },
      {
        "bitstring": "00000010",
        "count": 16,
        "probability": 0.008,
        "energy": 1.0,
        "active_states": [
          "P"
        ]
      },
      {
        "bitstring": "00111100",
        "count": 16,
        "probability": 0.008,
        "energy": 5.1,
        "active_states": [
          "G",
          "C",
          "B",
          "S"
        ]
      }
    ],
    "most_probable": {
      "bitstring": "10000100",
      "energy": 0.5
    }
  },
  "hachimoji_result": {
    "primary_state": "A",
    "primary_greek": "\u03a6",
    "description": "trivial \u2014 lowest energy basin",
    "active_states": [
      "A",
      "S"
    ],
    "hamming_weight": 2
  },
  "validation": {
    "exact": {
      "solution": [
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0
      ],
      "objective": -1.0,
      "degeneracy": 1,
      "primary_state": "A",
      "status": "exact"
    },
    "classical_solver": {
      "solution": [
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0
      ],
      "objective": -1.0,
      "primary_state": "A",
      "status": "SA_heuristic",
      "runtime_s": 0.4915
    }
  },
  "agreement": {
    "qaoa_matches_exact": true,
    "classical_matches_exact": true
  },
  "runtime": {
    "optimization_s": 0.7084,
    "total_s": 1.219
  }
}