""" Experimental Validation Framework - Fractal Compass v4.0 ======================================================== Connects theoretical predictions to experimental benchmarks: - IBM Quantum system parameters - Diamond NV center measurements - LHC bounds on extra dimensions - Atomic clock precision tests - Gravitational wave detector sensitivity References: [1] IBM Quantum Backend Properties [2] Doherty et al., Phys.Rep.528:1-45,2013 (Diamond NV) [3] CMS Collaboration, JHEP 1807:208,2018 (Extra dimensions) [4] LIGO Collaboration, Phys.Rev.Lett.116:061102,2016 """ import numpy as np import scipy.constants as const import scipy.stats from typing import Dict, List, Tuple, Any from dataclasses import dataclass import matplotlib.pyplot as plt @dataclass class ExperimentalBenchmark: """Container for experimental benchmark data.""" name: str system_type: str parameters: Dict[str, float] uncertainties: Dict[str, float] reference: str validation_method: str class ExperimentalValidator: """ Validates theoretical predictions against experimental benchmarks. Implements multiple validation protocols: 1. Parameter consistency checks 2. Statistical significance testing 3. Systematic error analysis 4. Cross-validation with independent experiments """ def __init__(self): self.benchmarks = self._load_experimental_benchmarks() self.validation_results = {} def _load_experimental_benchmarks(self) -> List[ExperimentalBenchmark]: """Load validated experimental benchmarks from literature.""" benchmarks = [] # IBM Quantum Systems (from hardware specifications) ibm_benchmark = ExperimentalBenchmark( name="IBM_Quantum_Lima", system_type="superconducting_transmon", parameters={ 'T1_mean': 121e-6, # Relaxation time (s) 'T2_mean': 89e-6, # Dephasing time (s) 'single_gate_error': 3.2e-4, 'cx_gate_error': 7.8e-3, 'readout_error': 2.1e-2, 'frequency': 4.97e9, # Qubit frequency (Hz) 'anharmonicity': -330e6 # MHz }, uncertainties={ 'T1_std': 15e-6, 'T2_std': 12e-6, 'single_gate_std': 0.5e-4, 'cx_gate_std': 1.2e-3 }, reference="IBM Quantum Backend Properties, 2024", validation_method="process_tomography" ) benchmarks.append(ibm_benchmark) # Diamond NV Centers (from Doherty et al.) nv_benchmark = ExperimentalBenchmark( name="Diamond_NV_Ensemble", system_type="solid_state_spin", parameters={ 'T1_bulk': 6e-3, # Bulk diamond T1 (s) 'T2_bulk': 1.8e-3, # Bulk T2 (s) 'T2_echo': 2.3e-3, # Echo coherence (s) 'zero_field_splitting': 2.87e9, # Hz 'gyromagnetic_ratio': 28.024e9, # Hz/T 'hyperfine_coupling': 2.16e6 # Hz (14N) }, uncertainties={ 'T1_std': 0.5e-3, 'T2_std': 0.2e-3, 'T2_echo_std': 0.3e-3 }, reference="Doherty et al., Phys.Rep.528:1-45,2013", validation_method="ramsey_spectroscopy" ) benchmarks.append(nv_benchmark) # LHC Extra Dimension Bounds (from CMS) lhc_benchmark = ExperimentalBenchmark( name="CMS_LED_Search", system_type="collider_physics", parameters={ 'led_scale_limit': 5.3e12, # GeV (95% CL) 'rs1_mass_limit': 4.1e12, # GeV (RS graviton) 'add_scale_limit': 7.2e12, # GeV (ADD model) 'center_mass_energy': 13e12, # GeV (13 TeV) 'integrated_luminosity': 137e15 # pb^-1 }, uncertainties={ 'led_scale_std': 0.3e12, 'systematic_error': 0.15 # 15% systematic }, reference="CMS Collaboration, JHEP 1807:208,2018", validation_method="missing_energy_analysis" ) benchmarks.append(lhc_benchmark) # LIGO Gravitational Waves (sensitivity to extra dimensions) ligo_benchmark = ExperimentalBenchmark( name="LIGO_O3_Sensitivity", system_type="gravitational_interferometer", parameters={ 'strain_sensitivity': 1e-23, # Characteristic strain 'frequency_range': [20, 2000], # Hz 'arm_length': 4000, # meters 'laser_power': 200, # watts 'mirror_mass': 40 # kg }, uncertainties={ 'calibration_error': 0.05, # 5% calibration uncertainty 'statistical_error': 1e-24 # Statistical noise floor }, reference="LIGO Collaboration, Phys.Rev.D100:062001,2019", validation_method="matched_filter_analysis" ) benchmarks.append(ligo_benchmark) return benchmarks def validate_quantum_parameters(self, theoretical_params: Dict[str, float]) -> Dict[str, Any]: """ Validate quantum decoherence parameters against experimental benchmarks. Args: theoretical_params: Dictionary of theoretical predictions Returns: Validation results with statistical significance """ results = {} # Find relevant quantum benchmarks quantum_benchmarks = [b for b in self.benchmarks if b.system_type in ['superconducting_transmon', 'solid_state_spin']] for benchmark in quantum_benchmarks: benchmark_results = {} # T1 validation if 'T1' in theoretical_params and 'T1_mean' in benchmark.parameters: t1_theory = theoretical_params['T1'] t1_exp = benchmark.parameters['T1_mean'] t1_err = benchmark.uncertainties['T1_std'] # Z-score for significance testing z_score = abs(t1_theory - t1_exp) / t1_err p_value = 2 * (1 - scipy.stats.norm.cdf(abs(z_score))) benchmark_results['T1'] = { 'theoretical': t1_theory, 'experimental': t1_exp, 'uncertainty': t1_err, 'z_score': z_score, 'p_value': p_value, 'consistent': p_value > 0.05 # 95% confidence } # T2 validation if 'T2' in theoretical_params and 'T2_mean' in benchmark.parameters: t2_theory = theoretical_params['T2'] t2_exp = benchmark.parameters['T2_mean'] t2_err = benchmark.uncertainties['T2_std'] z_score = abs(t2_theory - t2_exp) / t2_err p_value = 2 * (1 - scipy.stats.norm.cdf(abs(z_score))) benchmark_results['T2'] = { 'theoretical': t2_theory, 'experimental': t2_exp, 'uncertainty': t2_err, 'z_score': z_score, 'p_value': p_value, 'consistent': p_value > 0.05 } results[benchmark.name] = benchmark_results return results def validate_extra_dimension_bounds(self, theoretical_bounds: Dict[int, float]) -> Dict[str, Any]: """ Validate extra dimension compactification against LHC bounds. Args: theoretical_bounds: Dictionary mapping dimension -> scale (GeV) Returns: Validation results comparing theory vs experiment """ results = {} # Get LHC benchmark lhc_benchmark = next((b for b in self.benchmarks if b.name == "CMS_LED_Search"), None) if not lhc_benchmark: return {'error': 'No LHC benchmark found'} # LED scale comparison if 'led_scale' in theoretical_bounds: theory_scale = theoretical_bounds['led_scale'] exp_limit = lhc_benchmark.parameters['led_scale_limit'] exp_error = lhc_benchmark.uncertainties['led_scale_std'] # Check if theory respects experimental bound consistent = theory_scale < exp_limit significance = (exp_limit - theory_scale) / exp_error results['led_validation'] = { 'theoretical_scale': theory_scale, 'experimental_limit': exp_limit, 'uncertainty': exp_error, 'consistent_with_bounds': consistent, 'significance': significance, 'safety_margin': (exp_limit - theory_scale) / exp_limit } # RS graviton mass validation if 'rs_graviton_mass' in theoretical_bounds: theory_mass = theoretical_bounds['rs_graviton_mass'] exp_limit = lhc_benchmark.parameters['rs1_mass_limit'] results['rs_validation'] = { 'theoretical_mass': theory_mass, 'experimental_limit': exp_limit, 'consistent': theory_mass > exp_limit, # Mass should be above limit 'exclusion_power': theory_mass / exp_limit } return results def cross_validate_systems(self, system1_results: Dict, system2_results: Dict) -> Dict[str, Any]: """ Cross-validate results between different experimental systems. Checks for consistency between different physical implementations of the same theoretical framework. """ cross_validation = {} # Find common parameters common_params = set(system1_results.keys()) & set(system2_results.keys()) for param in common_params: if isinstance(system1_results[param], dict) and isinstance(system2_results[param], dict): if 'theoretical' in system1_results[param] and 'theoretical' in system2_results[param]: val1 = system1_results[param]['theoretical'] val2 = system2_results[param]['theoretical'] err1 = system1_results[param].get('uncertainty', 0) err2 = system2_results[param].get('uncertainty', 0) # Combined uncertainty combined_err = np.sqrt(err1**2 + err2**2) # Consistency test if combined_err > 0: consistency_z = abs(val1 - val2) / combined_err consistent = consistency_z < 2.0 # 2σ criterion else: consistent = abs(val1 - val2) < 1e-10 consistency_z = 0 cross_validation[param] = { 'value1': val1, 'value2': val2, 'combined_uncertainty': combined_err, 'consistency_z': consistency_z, 'consistent': consistent } return cross_validation def generate_validation_report(self, all_results: Dict[str, Any]) -> str: """Generate comprehensive validation report.""" report = [] report.append("EXPERIMENTAL VALIDATION REPORT") report.append("=" * 50) report.append("") # Summary statistics total_tests = 0 passed_tests = 0 for system, results in all_results.items(): report.append(f"System: {system}") report.append("-" * 30) if isinstance(results, dict): for param, data in results.items(): if isinstance(data, dict) and 'consistent' in data: total_tests += 1 if data['consistent']: passed_tests += 1 status = "PASS" else: status = "FAIL" if 'z_score' in data: report.append(f"{param}: {status} (Z={data['z_score']:.2f}, p={data.get('p_value', 0):.3f})") else: report.append(f"{param}: {status}") report.append("") # Overall summary pass_rate = passed_tests / total_tests if total_tests > 0 else 0 report.append(f"OVERALL VALIDATION: {passed_tests}/{total_tests} tests passed ({pass_rate:.1%})") if pass_rate >= 0.8: report.append("CONCLUSION: Theory consistent with experimental data") elif pass_rate >= 0.6: report.append("CONCLUSION: Partial consistency, requires refinement") else: report.append("CONCLUSION: Theory inconsistent with experimental data") return "\n".join(report)