{
  "laboratory_frame": {
    "Omega_over_omega_0": [
      0.02,
      0.05,
      0.1,
      0.2,
      0.3
    ],
    "fine_steps_per_carrier_cycle": 1600,
    "hamiltonian": "H/hbar = omega_0 sigma_z/2 + Omega cos(omega_L t + phase) sigma_x",
    "integrator": "exponential midpoint with exact frozen 2x2 Hamiltonian exponential",
    "integrator_global_order": 2,
    "omega_0": 1.0,
    "omega_L": 1.0,
    "samples": 401,
    "tau_range": [
      0.0,
      6.283185307179586
    ],
    "validation": {
      "RWA_discrepancy_at_strongest_drive": 0.07874839249654197,
      "RWA_discrepancy_at_weakest_drive": 0.005041845119929778,
      "checks": {
        "RWA_error_grows_over_test_range": true,
        "midpoint_converged": true,
        "physical_error_resolved": true,
        "unitary_steps": true
      },
      "largest_fine_norm_error": 1.6475709685437323e-13,
      "largest_medium_fine_population_difference": 4.651776076003422e-06,
      "weak_drive_discrepancy_to_numerical_error_ratio": 1083.8537877905515
    }
  },
  "license": "MIT",
  "limitations": [
    "two-state projection is assumed rather than derived",
    "closed-system unitary dynamics only",
    "no relaxation, dephasing, leakage, motion, or ensemble averaging",
    "the full laboratory-frame comparison uses a monochromatic drive",
    "pulse calibration and readout errors are absent"
  ],
  "outputs": [
    "time-dependent-two-level-rabi.csv",
    "time-dependent-two-level-rwa-comparison.csv",
    "time-dependent-two-level-pulse-area.csv",
    "time-dependent-two-level-ramsey.csv",
    "time-dependent-two-level-convergence.csv",
    "time-dependent-two-level-metadata.json"
  ],
  "provenance": {
    "Bloch_Siegert": {
      "doi": "10.1103/PhysRev.57.522"
    },
    "Floquet_two_state": {
      "doi": "10.1103/PhysRev.138.B979"
    },
    "Rabi": {
      "doi": "10.1103/PhysRev.51.652"
    },
    "Ramsey": {
      "doi": "10.1103/PhysRev.78.695"
    }
  },
  "pulse_area": {
    "area_range": [
      0.0,
      12.566370614359172
    ],
    "duration": 1.0,
    "gaussian_sigma": 0.15,
    "gaussian_steps": 1200,
    "off_resonant_test_delta": 2.0,
    "samples": 161,
    "square_amplitude": "area / duration",
    "validation": {
      "checks": {
        "gaussian_area_theorem": true,
        "off_resonant_shape_dependence_resolved": true,
        "square_area_theorem": true,
        "unit_norm": true
      },
      "max_off_resonant_square_minus_gaussian": 0.25921254090017753,
      "max_resonant_gaussian_minus_area_law": 7.305050864214735e-08,
      "max_resonant_square_minus_area_law": 2.220446049250313e-16,
      "max_state_norm_error": 6.550315845288424e-14
    }
  },
  "rabi": {
    "Omega": 1.0,
    "detuning_over_Omega": [
      0.0,
      0.5,
      1.0
    ],
    "samples": 401,
    "tau_range": [
      0.0,
      12.566370614359172
    ],
    "validation": {
      "checks": {
        "analytic_population": true,
        "unit_norm": true
      },
      "max_matrix_minus_analytic_probability": 2.220446049250313e-16,
      "max_state_norm_error": 3.3306690738754696e-16
    }
  },
  "ramsey": {
    "detuning_range": [
      -1.0,
      1.0
    ],
    "free_time": 10.0,
    "pulse_Omega": 4.0,
    "pulse_area": 1.5707963267948966,
    "pulse_duration": 0.39269908169872414,
    "samples": 401,
    "validation": {
      "checks": {
        "ideal_formula": true,
        "resonant_sequence": true,
        "unit_norm": true,
        "zero_crossing_error_signal": true
      },
      "finite_error_signal_slope_at_resonance": 10.495177189787293,
      "max_finite_minus_instantaneous_probability": 0.1915320567892731,
      "max_ideal_matrix_minus_formula": 5.551115123125783e-16,
      "max_state_norm_error": 8.881784197001252e-16,
      "on_resonance_finite_error_signal": 0.0,
      "on_resonance_finite_population": 1.0000000000000004
    }
  },
  "runtime": {
    "numpy": "2.3.5",
    "platform": "Windows-11-10.0.26200-SP0",
    "python": "3.12.13",
    "random_seed": null
  },
  "scope": {
    "basis": [
      "excited",
      "ground"
    ],
    "claim": "closed-system propagator and approximation benchmark, not a species-specific prediction",
    "detuning_convention": "delta = omega_0 - omega_L",
    "sigma_z_eigenvalues": [
      1,
      -1
    ],
    "system": "generic coherent two-level system",
    "units": {
      "frequency": "declared angular-frequency unit",
      "hbar": 1.0,
      "time": "reciprocal angular-frequency unit"
    }
  },
  "validation": {
    "all_checks_passed": true,
    "sections": {
      "pulse_area": {
        "gaussian_area_theorem": true,
        "off_resonant_shape_dependence_resolved": true,
        "square_area_theorem": true,
        "unit_norm": true
      },
      "rabi": {
        "analytic_population": true,
        "unit_norm": true
      },
      "ramsey": {
        "ideal_formula": true,
        "resonant_sequence": true,
        "unit_norm": true,
        "zero_crossing_error_signal": true
      },
      "rwa": {
        "RWA_error_grows_over_test_range": true,
        "midpoint_converged": true,
        "physical_error_resolved": true,
        "unitary_steps": true
      }
    }
  }
}