{ "cells": [ { "celltype": "markdown", "metadata": {}, "source": [ "# Eigenvector Clustering & 3D Interactive Stability Basins\n", "\n", "This notebook analyzes your SD&N resonance permutations by:\n", "- Building coupling matrices\n", "- Computing eigenvectors and spectral radii\n", "- Clustering permutations by eigenvector similarity\n", "- Visualizing stability basins in interactive 3D plots\n", "\n", "### Requirements:\n", "- numpy\n", "- scikit-learn\n", "- plotly" ] }, { "celltype": "code", "metadata": {}, "source": [ "# Imports\n", "import numpy as np\n", "import plotly.express as px\n", "from itertools import permutations\n", "from sklearn.cluster import AgglomerativeClustering\n", "from sklearn.metrics.pairwise import cosinesimilarity\n" ] }, { "celltype": "code", "metadata": {}, "source": [ "# Resonance codes\n", "codes = np.array([7146, 1467, 4671, 6714])\n", "\n", "def buildcouplingmatrix(order):\n", " n = len(order)\n", " matrix = np.zeros((n, n))\n", " for i in range(n):\n", " for j in range(n):\n", " if i == j:\n", " matrix[i, j] = 1.0 # Self coupling\n", " else:\n", " diff = abs(order[i] - order[j])\n", " matrix[i, j] = 1 / (diff + 1e-3)\n", " return matrix\n" ] }, { "celltype": "code", "metadata": {}, "source": [ "# Get all permutations\n", "perms = list(permutations(codes))\n", "\n", "# Compute eigenvalues and eigenvectors\n", "eigenvectors = []\n", "spectralradii = []\n", "for perm in perms:\n", " matrix = buildcouplingmatrix(np.array(perm))\n", " eigvals, eigvecs = np.linalg.eig(matrix)\n", " spectralradii.append(np.max(np.abs(eigvals)))\n", " # Flatten real parts of eigenvectors for similarity\n", " eigvecsflat = eigvecs.real.flatten()\n", " eigenvectors.append(eigvecsflat)\n", "\n", "eigenvectors = np.array(eigenvectors)\n" ] }, { "celltype": "code", "metadata": {}, "source": [ "# Compute cosine similarity matrix between eigenvector sets\n", "similaritymatrix = cosinesimilarity(eigenvectors)\n", "\n", "# Cluster permutations using Agglomerative Clustering\n", "clustering = AgglomerativeClustering(nclusters=3, affinity='precomputed', linkage='average')\n", "labels = clustering.fitpredict(1 - similaritymatrix) # distance = 1 - similarity\n" ] }, { "celltype": "code", "metadata": {}, "source": [ "# Prepare data for 3D plot\n", "import plotly.express as px\n", "\n", "x = list(range(len(perms)))\n", "y = spectralradii\n", "z = labels\n", "\n", "# Create hover text for permutations\n", "hovertext = [str(perm) for perm in perms]\n", "\n", "# Plot interactive 3D scatter\n", "fig = px.scatter3d(\n", " x=x,\n", " y=y,\n", " z=z,\n", " color=z.astype(str),\n", " labels={'x': 'Permutation Index', 'y': 'Spectral Radius', 'z': 'Cluster Label'},\n", " hovername=hovertext,\n", " title=\"3D Interactive Stability Basin & Eigenvector Clustering\"\n", ")\n", "\n", "fig.updatetraces(marker=dict(size=8))\n", "fig.show()" ] } ], "metadata": { "kernelspec": { "displayname": "Python 3", "language": "python", "name": "python3" }, "languageinfo": { "name": "python", "version": "3.10" } }, "nbformat": 4, "nbformatminor": 5 } # Fast calculation without logging anglerad = math.radians(angledeg) signaturevalue = self.calculatenumericalsignaturevalue(signature) Save this JSON as EigenvectorClusteringStabilityBasins.ipynb. • Upload it to IBM Quantum Lab or any Jupyter environment. • Run cells sequentially; the final output is an interactive 3D plot.

# SDKP time τ_s
use_sdkp_time = self.config['parameters'].get('use_sdkp_time', False)
if use_sdkp_time:
    size = self.config['parameters'].get('sdkp_size', 1.0)
    density = self.config['parameters'].get('sdkp_density', 1.0)
    rotation_velocity = self.config['parameters'].get('sdkp_rotation_velocity', 1.0)
    tau_s = size * density * rotation_velocity
else:
    tau_s = 0.0

# Component calculations
C_SDN = abs(np.cos(angle_rad)) * signature_value
C_V = (2 * signature_value) - 1
VEI_delta = 1 - abs(C_V)

qf_angle = angle_rad * 2 + tau_s if use_sdkp_time else angle_rad * 2
QF_delta = abs(np.sin(qf_angle) - signature_value)

# QCC entropy
use_qcc_entropy = self.config['parameters'].get('use_qcc_entropy', False)
if use_qcc_entropy:
    entropy = self.config['parameters'].get('qcc_entropy', 1.0)
    epsilon_qcc = entropy / tau_s if use_sdkp_time and tau_s > 0 else entropy
else:
    epsilon_qcc = 1.0

QF_delta_weighted = QF_delta * epsilon_qcc

# Apply mapping
mapping_type = self.config['parameters'].get('mapping_type', 'linear')
C_SDN_mapped = self.apply_mapping_function(C_SDN, mapping_type)
VEI_delta_mapped = self.apply_mapping_function(VEI_delta, mapping_type)
QF_delta_mapped = self.apply_mapping_function(QF_delta_weighted, mapping_type)

# Weighted combination
weights = self.config['parameters']['lambda_weights']
entanglement_value = (
    weights['C_SDN'] * C_SDN_mapped +
    weights['VEI_delta'] * VEI_delta_mapped +
    weights['QF_delta'] * QF_delta_mapped
)

components = {
    'C_SDN_raw': C_SDN,
    'VEI_delta_raw': VEI_delta,
    'QF_delta_raw': QF_delta,
    'QF_delta_weighted': QF_delta_weighted,
    'C_SDN_mapped': C_SDN_mapped,
    'VEI_delta_mapped': VEI_delta_mapped,
    'QF_delta_mapped': QF_delta_mapped,
    'signature_value': signature_value,
    'tau_s': tau_s,
    'epsilon_qcc': epsilon_qcc
}

return entanglement_value, components

def calculateentanglementmeasuredetailed(self, angledeg: float, signature: str) -> Tuple[float, Dict[str, float]]: """Your original detailed method with full logging""" self.log(f"\n--- Calculating Entanglement for Angle {angle_deg}° and Signature '{signature}' ---")

angle_rad = math.radians(angle_deg)
self.log(f"Step 1: Convert angle {angle_deg}° to radians: {angle_rad:.4f} rad (radians are dimensionless angles used for trig functions)")

signature_value = self.calculate_numerical_signature_value(signature)
self.log(f"Step 2: Calculated numerical signature value for '{signature}': {signature_value:.4f} (dimensionless normalized value derived from signature digits)")

# SDKP time τ_s: Size × Density × Rotation Velocity
use_sdkp_time = self.config['parameters'].get('use_sdkp_time', False)
if use_sdkp_time:
    size = self.config['parameters'].get('sdkp_size', 1.0)  # meters (m)
    density = self.config['parameters'].get('sdkp_density', 1.0)  # kg/m³
    rotation_velocity = self.config['parameters'].get('sdkp_rotation_velocity', 1.0)  # radians/second (rad/s)
    tau_s = size * density * rotation_velocity
    self.log(f"SDKP time (τ_s) calculated: τ_s = Size (m) × Density (kg/m³) × Rotation Velocity (rad/s) = {tau_s:.4f} [units: m·kg/m³·rad/s]")
    self.log("Note: τ_s has composite units, representing a scale of time within SDKP framework")
else:
    tau_s = 0.0
    self.log("SDKP time (τ_s) disabled; using standard angular calculations without SDKP time scaling.")

# C_SDN — dimensionless correlation between polarization angle and signature
C_SDN = abs(np.cos(angle_rad)) * signature_value
self.log(f"Step 3a (C_SDN): |cos(angle_rad)| × signature_value = {C_SDN:.4f} (dimensionless correlation factor)")

# VEI_delta — vibrational mismatch (dimensionless)
C_V = (2 * signature_value) - 1  # maps [0,1] to [-1,1]
VEI_delta = 1 - abs(C_V)
self.log(f"Step 3b (VEI_delta): 1 - |2×signature_value - 1| = {VEI_delta:.4f} (dimensionless vibrational entanglement index)")

# QF_delta — quantum number flow mismatch
qf_angle = angle_rad * 2 + tau_s if use_sdkp_time else angle_rad * 2
self.log(f"Step 3c (QF_delta) calculation uses angle doubled and adds τ_s phase shift if enabled:")
self.log(f"  qf_angle = angle_rad × 2 {'+ τ_s' if use_sdkp_time else ''} = {qf_angle:.4f} radians")
QF_delta = abs(np.sin(qf_angle) - signature_value)
self.log(f"QF_delta = |sin(qf_angle) - signature_value| = {QF_delta:.4f} (dimensionless mismatch)")

# QCC entropy density ε_QCC (bits per SDKP time)
use_qcc_entropy = self.config['parameters'].get('use_qcc_entropy', False)
if use_qcc_entropy:
    entropy = self.config['parameters'].get('qcc_entropy', 1.0)  # bits of entropy
    if use_sdkp_time and tau_s > 0:
        epsilon_qcc = entropy / tau_s
        self.log(f"QCC entropy density (ε_QCC) = entropy (bits) / τ_s = {entropy:.4f} bits / {tau_s:.4f} SDKP time units = {epsilon_qcc:.4f} bits/SDKP time")
    else:
        epsilon_qcc = entropy
        self.log(f"QCC entropy (ε_QCC) used as raw bits: {epsilon_qcc:.4f} bits (no SDKP time scaling)")
else:
    epsilon_qcc = 1.0
    self.log("QCC entropy weighting disabled; ε_QCC set to 1 (no effect).")

# Apply ε_QCC as weighting multiplier on QF_delta (dimensionless)
QF_delta_weighted = QF_delta * epsilon_qcc
self.log(f"Weighted QF_delta with ε_QCC: {QF_delta:.4f} × {epsilon_qcc:.4f} = {QF_delta_weighted:.4f} (dimensionless)")

# Apply mapping transformations to each component
mapping_type = self.config['parameters'].get('mapping_type', 'linear')
self.log(f"Step 4: Applying '{mapping_type}' mapping function to components.")

C_SDN_mapped = self.apply_mapping_function(C_SDN, mapping_type)
self.log(f"  Mapped C_SDN: {C_SDN:.4f} -> {C_SDN_mapped:.4f}")

VEI_delta_mapped = self.apply_mapping_function(VEI_delta, mapping_type)
self.log(f"  Mapped VEI_delta: {VEI_delta:.4f} -> {VEI_delta_mapped:.4f}")

QF_delta_mapped = self.apply_mapping_function(QF_delta_weighted, mapping_type)
self.log(f"  Mapped Weighted QF_delta: {QF_delta_weighted:.4f} -> {QF_delta_mapped:.4f}")

# Retrieve lambda weights for weighted sum
weights = self.config['parameters']['lambda_weights']
self.log(f"Step 5: Applying lambda weights: C_SDN={weights['C_SDN']:.2f}, VEI_delta={weights['VEI_delta']:.2f}, QF_delta={weights['QF_delta']:.2f}")

# Final entanglement value as weighted sum of mapped components
entanglement_value = (
    weights['C_SDN'] * C_SDN_mapped +
    weights['VEI_delta'] * VEI_delta_mapped +
    weights['QF_delta'] * QF_delta_mapped
)
self.log(f"  Calculation: ({weights['C_SDN']:.2f} × {C_SDN_mapped:.4f}) + "
         f"({weights['VEI_delta']:.2f} × {VEI_delta_mapped:.4f}) + "
         f"({weights['QF_delta']:.2f} × {QF_delta_mapped:.4f})")
self.log(f"  Final Entanglement Value: {entanglement_value:.4f} (dimensionless)")

components = {
    'C_SDN_raw': C_SDN,
    'VEI_delta_raw': VEI_delta,
    'QF_delta_raw': QF_delta,
    'QF_delta_weighted': QF_delta_weighted,
    'C_SDN_mapped': C_SDN_mapped,
    'VEI_delta_mapped': VEI_delta_mapped,
    'QF_delta_mapped': QF_delta_mapped,
    'signature_value': signature_value,
    'tau_s': tau_s,
    'epsilon_qcc': epsilon_qcc
}pip install qiskit}from qiskit import QuantumCircuit, Aer, transpile, assemble

from qiskit.quantuminfo import Statevector, partialtrace, entropy, concurrence

Build a Bell state: |Φ+> = (|00> + |11>) / √2

qc = QuantumCircuit(2) qc.h(0) # Hadamard on qubit 0 qc.cx(0, 1) # CNOT from qubit 0 to 1

Simulate the statevector

simulator = Aer.getbackend("statevectorsimulator") tqc = transpile(qc, simulator) qobj = assemble(tqc) result = simulator.run(qobj).result() state = result.get_statevector()

Get reduced density matrix (trace out one qubit)

reducedrho = partialtrace(state, [1])

Calculate Entanglement Entropy (von Neumann)

ententropy = entropy(reducedrho, base=2)

Calculate Concurrence

conc = concurrence(state)

print("Entanglement Entropy (von Neumann):", ententropy) print("Concurrence:", conc)EAB = w1 * SDNsim + w2 * ΔVEI + w3 * ΔQF + w4 * HQCC Input Case True Concurrence Your EAB Output Bell state ( Φ+⟩) 1.0 Separable ( 00⟩) 0.0 Mixed state 0.3–0.7 (varied) ?

return entanglement_value, components

def parametersensitivityanalysis(self, samplesize: int = 1000) -> SensitivityResults: """ Comprehensive parameter sensitivity analysis using Latin Hypercube Sampling and Sobol sensitivity analysis """ self.log("Starting comprehensive parameter sensitivity analysis...") starttime = time.time()

# Define parameter ranges for sensitivity analysis
param_ranges = {
    'C_SDN_weight': (0.1, 0.8),
    'VEI_delta_weight': (0.1, 0.8), 
    'QF_delta_weight': (0.1, 0.8),
    'sdkp_size': (0.1, 10.0),
    'sdkp_density': (0.1, 10.0),
    'sdkp_rotation_velocity': (0.1, 10.0),
    'qcc_entropy': (0.1, 5.0),
    'angle_deg': (0, 180),
    'signature_complexity': (1, 15)  # Number of digits in signature
}

# Generate Latin Hypercube samples
n_params = len(param_ranges)
lhs_samples = self._latin_hypercube_sampling(sample_size, n_params)

# Scale samples to parameter ranges
param_names = list(param_ranges.keys())
scaled_samples = np.zeros_like(lhs_samples)

for i, param_name in enumerate(param_names):
    min_val, max_val = param_ranges[param_name]
    scaled_samples[:, i] = min_val + lhs_samples[:, i] * (max_val - min_val)

# Calculate entanglement values for all samples
entanglement_values = []
component_values = {comp: [] for comp in ['C_SDN_mapped', 'VEI_delta_mapped', 'QF_delta_mapped']}

for sample in scaled_samples:
    # Create temporary config for this sample
    temp_config = self._create_temp_config_from_sample(sample, param_names)
    temp_simulator = OptimizedQuantumEntanglementSimulator(temp_config)

    # Calculate entanglement for sample
    angle = sample[param_names.index('angle_deg')]
    sig_complexity = int(sample[param_names.index('signature_complexity')])
    signature = '1' * sig_complexity  # Simple signature of given complexity

    entanglement_val, components = temp_simulator.calculate_entanglement_measure_optimized(
        angle, signature, detailed_logging=False
    )

    entanglement_values.append(entanglement_val)
    for comp_name in component_values:
        component_values[comp_name].append(components[comp_name])

entanglement_values = np.array(entanglement_values)

# Calculate Sobol indices (first-order sensitivity indices)
parameter_impacts = {}
for i, param_name in enumerate(param_names):
    sensitivity = self._calculate_sobol_index(scaled_samples[:, i], entanglement_values)
    parameter_impacts[param_name] = float(sensitivity)

# Calculate interaction effects (second-order)
interaction_effects = {}
for i in range(len(param_names)):
    for j in range(i+1, len(param_names)):
        param1, param2 = param_names[i], param_names[j]
        interaction = self._calculate_interaction_effect(
            scaled_samples[:, i], scaled_samples[:, j], entanglement_values
        )
        interaction_effects[f"{param1}_x_{param2}"] = float(interaction)

# Component sensitivities
component_sensitivities = {}
for comp_name, comp_values in component_values.items():
    comp_values = np.array(comp_values)
    comp_sensitivities = {}
    for i, param_name in enumerate(param_names):
        sensitivity = self._calculate_sobol_index(scaled_samples[:, i], comp_values)
        comp_sensitivities[param_name] = float(sensitivity)
    component_sensitivities[comp_name] = comp_sensitivities

# Correlation matrix
all_data = np.column_stack([scaled_samples, entanglement_values])
correlation_matrix = np.corrcoef(all_data.T)

# Total variance explained
total_variance_explained = sum(parameter_impacts.values())

analysis_time = time.time() - start_time
self.log(f"Parameter sensitivity analysis completed in {analysis_time:.2f} seconds")

return SensitivityResults(
    parameter_impacts=parameter_impacts,
    interaction_effects=interaction_effects,
    component_sensitivities=component_sensitivities,
    correlation_matrix=correlation_matrix,
    parameter_names=param_names + ['entanglement'],
    total_variance_explained=total_variance_explained
)

def latinhypercubesampling(self, nsamples: int, ndimensions: int) -> np.ndarray: """Generate Latin Hypercube samples""" samples = np.zeros((nsamples, n_dimensions))

for i in range(n_dimensions):
    samples[:, i] = (np.random.permutation(n_samples) + np.random.random(n_samples)) / n_samples

return samples

def createtempconfigfromsample(self, sample: np.ndarray, paramnames: List[str]) -> Dict[str, Any]: """Create temporary configuration from parameter sample""" base_config = self.config.copy()

# Normalize weights to sum to 1
c_sdn_weight = sample[param_names.index('C_SDN_weight')]
vei_weight = sample[param_names.index('VEI_delta_weight')]
qf_weight = sample[param_names.index('QF_delta_weight')]
total_weight = c_sdn_weight + vei_weight + qf_weight

base_config['parameters'] = base_config.get('parameters', {}).copy()
base_config['parameters'].update({
    'lambda_weights': {
        'C_SDN': c_sdn_weight / total_weight,
        'VEI_delta': vei_weight / total_weight,
        'QF_delta': qf_weight / total_weight
    },
    'use_sdkp_time': True,
    'sdkp_size': sample[param_names.index('sdkp_size')],
    'sdkp_density': sample[param_names.index('sdkp_density')],
    'sdkp_rotation_velocity': sample[param_names.index('sdkp_rotation_velocity')],
    'use_qcc_entropy': True,
    'qcc_entropy': sample[param_names.index('qcc_entropy')],
    'logging': False  # Disable logging for performance
})

return base_config

def calculatesobolindex(self, paramvalues: np.ndarray, outputvalues: np.ndarray) -> float: """Calculate first-order Sobol sensitivity index""" try: # Sort by parameter values sortedindices = np.argsort(paramvalues) sortedoutput = outputvalues[sortedindices]

    # Calculate conditional variances
    n_bins = min(10, len(param_values) // 10)
    if n_bins < 2:
        return 0.0

    bin_size = len(param_values) // n_bins
    bin_vars = []

    for i in range(n_bins):
        start_idx = i * bin_size
        end_idx = start_idx + bin_size if i < n_bins - 1 else len(param_values)
        bin_data = sorted_output[start_idx:end_idx]
        if len(bin_data) > 1:
            bin_vars.append(np.var(bin_data))

    if not bin_vars:
        return 0.0

    # Sobol index approximation
    total_var = np.var(output_values)
    if total_var == 0:
        return 0.0

    conditional_var = np.mean(bin_vars)
    sobol_index = 1 - (conditional_var / total_var)

    return max(0.0, min(1.0, sobol_index))  # Clamp to [0,1]

except Exception:
    return 0.0

def calculateinteractioneffect(self, param1: np.ndarray, param2: np.ndarray, output: np.ndarray) -> float: """Calculate second-order interaction effect""" try: # Create 2D grid for interaction analysis nbins = 5

    # Discretize parameters
    p1_bins = np.digitize(param1, np.linspace(param1.min(), param1.max(), n_bins))
    p2_bins = np.digitize(param2, np.linspace(param2.min(), param2.max(), n_bins))

    # Calculate interaction variance
    interaction_effects = []
    for i in range(1, n_bins + 1):
        for j in range(1, n_bins + 1):
            mask = (p1_bins == i) & (p2_bins == j)
            if np.sum(mask) > 1:
                bin_output = output[mask]
                interaction_effects.append(np.var(bin_output))

    if not interaction_effects:
        return 0.0

    total_var = np.var(output)
    if total_var == 0:
        return 0.0

    interaction_var = np.mean(interaction_effects)
    return max(0.0, interaction_var / total_var)

except Exception:
    return 0.0

def runparallelsimulation(self, usemultiprocessing: bool = True, nworkers: int = None) -> OptimizedSimulationResults: """ Run simulation with parallel processing for performance optimization """ self.log("Starting optimized parallel simulation...") start_time = time.time()

angles = self.config['parameters']['polarization_angles_deg']
signatures = self.config['parameters']['numerical_signatures']

# Pre-compute signature values
signature_values = self.calculate_numerical_signature_value_vectorized(signatures)

# Create parameter combinations
param_combinations = list(product(angles, signatures))

# Determine number of workers
if n_workers is None:
    n_workers = min(mp.cpu_count(), len(param_combinations))

self.log(f"Processing {len(param_combinations)} combinations using {n_workers} workers")

# Choose executor based on use_multiprocessing flag
executor_class = ProcessPoolExecutor if use_multiprocessing else ThreadPoolExecutor

all_entanglement_values = []
all_correlation_coefficients = []
numerical_mappings = {}
polarization_data = []

# Process in batches for memory efficiency
batch_size = max(1, len(param_combinations) // n_workers)

with executor_class(max_workers=n_workers) as executor:
    # Submit angle-based batches
    angle_futures = {}

    for angle in angles:
        angle_combinations = [(a, s) for a, s in param_combinations if a == angle]
        future = executor.submit(self._process_angle_batch, angle_combinations)
        angle_futures[angle] = future

    # Collect results
    for angle, future in angle_futures.items():
        try:
            angle_results = future.result(timeout=300)  # 5 minute timeout

            angle_entanglements = angle_results['entanglements']
            angle_mappings = angle_results['mappings']

            all_entanglement_values.extend(angle_entanglements)
            numerical_mappings.update(angle_mappings)

            # Calculate correlation for this angle
            correlation = self._calculate_correlation_coefficient_fast(angle_entanglements)
            all_correlation_coefficients.append(correlation)

            # Create polarization data entry
            threshold = self.config['parameters'].get('entanglement_threshold', 0.75)
            angle_stats = {
                'angle_deg': angle,
                'entanglement_values': [float(x) for x in angle_entanglements],
                'mean_entanglement': float(np.mean(angle_entanglements)),
                'std_entanglement': float(np.std(angle_entanglements)),
                'min_entanglement': float(np.min(angle_entanglements)),
                'max_entanglement': float(np.max(angle_entanglements)),
                'correlation': float(correlation),
                'high_entanglement_count': sum(1 for e in angle_entanglements if e > threshold)
            }
            polarization_data.append(angle_stats)

        except Exception as e:
            self.log(f"Error processing angle {angle}: {e}", 'error')

# Calculate lambda contributions
lambda_contributions = self._calculate_lambda_contributions_fast(numerical_mappings)

# Run sensitivity analysis if requested
sensitivity_analysis = None
if self.config['parameters'].get('run_sensitivity_analysis', False):
    sample_size = self.config['parameters'].get('sensitivity_sample_size', 500)
    sensitivity_analysis = self.parameter_sensitivity_analysis(sample_size)

# Performance metrics
total_time = time.time() - start_time
performance_metrics = {
    'total_execution_time_seconds': total

``` Automatically synced with your v0.dev deployments

Overview

This repository will stay in sync with your deployed chats on v0.dev. Any changes you make to your deployed app will be automatically pushed to this repository from v0.dev.

Deployment

#!/usr/bin/env python3

“”” Quantum Entanglement Validation Framework

This script implements a scientific validation protocol to test whether any claimed quantum entanglement prediction system actually correlates with real quantum mechanical entanglement metrics.

Requirements: pip install qiskit matplotlib numpy scipy

Usage: python quantum_validation.py “””

import numpy as np import matplotlib.pyplot as plt from scipy.stats import pearsonr import warnings warnings.filterwarnings(‘ignore’)

Qiskit imports

from qiskit import QuantumCircuit, Aer, transpile, assemble from qiskit.quantuminfo import Statevector, partialtrace, entropy, concurrence from qiskit.quantuminfo import randomstatevector, DensityMatrix

class QuantumEntanglementValidator: “”” Scientific validation framework for quantum entanglement prediction systems. “””

``` def init(self): self.simulator = Aer.getbackend("statevectorsimulator") self.test_cases = [] self.results = []

def generatebellstate(self, phi=0, theta=0): """Generate parameterized Bell states for testing.""" qc = QuantumCircuit(2) qc.h(0) qc.cx(0, 1)

# Add rotation for parameterized states
if phi != 0:
    qc.rz(phi, 0)
if theta != 0:
    qc.ry(theta, 1)

return self._get_statevector(qc)

def generateseparablestate(self, alpha=0, beta=0): """Generate separable (non-entangled) states.""" qc = QuantumCircuit(2) qc.ry(alpha, 0) qc.ry(beta, 1) return self.getstatevector(qc)

def generatemixedstate(self, entanglementlevel=0.5): """Generate mixed states with varying entanglement.""" # Create a partially entangled state qc = QuantumCircuit(2) qc.h(0) qc.cry(2 * np.arccos(np.sqrt(entanglementlevel)), 0, 1) return self.getstatevector(qc)

def getstatevector(self, qc): """Helper to get statevector from quantum circuit.""" tqc = transpile(qc, self.simulator) qobj = assemble(tqc) result = self.simulator.run(qobj).result() return result.get_statevector()

def calculatetruemetrics(self, state): """Calculate true quantum entanglement metrics.""" # Convert to density matrix if needed if isinstance(state, Statevector): rho = DensityMatrix(state) else: rho = state

# Get reduced density matrix (trace out qubit 1)
reduced_rho = partial_trace(rho, [1])

# Calculate entanglement entropy (von Neumann)
ent_entropy = entropy(reduced_rho, base=2)

# Calculate concurrence
conc = concurrence(state)

return {
    'entropy': ent_entropy,
    'concurrence': conc,
    'state_description': str(type(state).__name__)
}

def mocksdkppredictor(self, state, photon_angle=0): """ Mock implementation of the SDKP formula for testing. This simulates what a claimed predictor might output.

E_AB = w1 * SDN_sim + w2 * ΔVEI + w3 * Δ_QF + w4 * H_QCC
"""
# Generate mock parameters (these would be the invented terms)
np.random.seed(42)  # For reproducibility

# Mock "SD&N similarity" - just use photon angle
sdn_sim = np.cos(photon_angle)**2

# Mock "Vibrational Entanglement Index" - random number
delta_vei = np.random.uniform(0, 1)

# Mock "Quantum Flow difference" - another random component
delta_qf = np.random.uniform(-0.5, 0.5)

# Mock "QCC Entropy" - yet another random term
h_qcc = np.random.uniform(0, 0.8)

# Mock weights
w1, w2, w3, w4 = 0.3, 0.2, 0.25, 0.25

# The claimed formula
e_ab = w1 * sdn_sim + w2 * delta_vei + w3 * delta_qf + w4 * h_qcc

return max(0, min(1, e_ab))  # Clamp to [0,1]

def runcomprehensivetest(self): """Run comprehensive validation test suite.""" print("🔬 Quantum Entanglement Validation Framework") print("=" * 50)

test_cases = []
true_metrics = []
predicted_scores = []

# Test Case 1: Perfect Bell States
print("\n📊 Test Case 1: Bell States (Maximally Entangled)")
for i in range(5):
    phi = i * np.pi / 4
    state = self.generate_bell_state(phi=phi)
    metrics = self.calculate_true_metrics(state)
    prediction = self.mock_sdkp_predictor(state, photon_angle=phi)

    test_cases.append(f"Bell φ={phi:.2f}")
    true_metrics.append(metrics['concurrence'])
    predicted_scores.append(prediction)

    print(f"  φ={phi:.2f}: True Concurrence={metrics['concurrence']:.3f}, "
          f"Predicted E_AB={prediction:.3f}")

# Test Case 2: Separable States
print("\n📊 Test Case 2: Separable States (No Entanglement)")
for i in range(5):
    alpha = i * np.pi / 8
    beta = (i + 1) * np.pi / 8
    state = self.generate_separable_state(alpha=alpha, beta=beta)
    metrics = self.calculate_true_metrics(state)
    prediction = self.mock_sdkp_predictor(state, photon_angle=alpha)

    test_cases.append(f"Separable α={alpha:.2f}")
    true_metrics.append(metrics['concurrence'])
    predicted_scores.append(prediction)

    print(f"  α={alpha:.2f}, β={beta:.2f}: True Concurrence={metrics['concurrence']:.3f}, "
          f"Predicted E_AB={prediction:.3f}")

# Test Case 3: Mixed States (Partial Entanglement)
print("\n📊 Test Case 3: Mixed States (Partial Entanglement)")
for level in [0.1, 0.3, 0.5, 0.7, 0.9]:
    state = self.generate_mixed_state(entanglement_level=level)
    metrics = self.calculate_true_metrics(state)
    prediction = self.mock_sdkp_predictor(state, photon_angle=0)

    test_cases.append(f"Mixed {level}")
    true_metrics.append(metrics['concurrence'])
    predicted_scores.append(prediction)

    print(f"  Level={level}: True Concurrence={metrics['concurrence']:.3f}, "
          f"Predicted E_AB={prediction:.3f}")

# Statistical Analysis
print("\n📈 Statistical Analysis")
print("=" * 30)

correlation, p_value = pearsonr(true_metrics, predicted_scores)
print(f"Pearson Correlation: {correlation:.4f}")
print(f"P-value: {p_value:.4f}")

# Validation Criteria
print(f"\n✅ Validation Criteria:")
print(f"  • Correlation > 0.9: {'✓' if correlation > 0.9 else '✗'} ({correlation:.4f})")
print(f"  • P-value < 0.05: {'✓' if p_value < 0.05 else '✗'} ({p_value:.4f})")
print(f"  • Bell states → High scores: {'✓' if np.mean(predicted_scores[:5]) > 0.7 else '✗'}")
print(f"  • Separable → Low scores: {'✓' if np.mean(predicted_scores[5:10]) < 0.3 else '✗'}")

# Overall Assessment
criteria_met = (correlation > 0.9 and p_value < 0.05 and 
               np.mean(predicted_scores[:5]) > 0.7 and 
               np.mean(predicted_scores[5:10]) < 0.3)

print(f"\n🎯 Overall Assessment:")
if criteria_met:
    print("✅ PASS: The predictor shows strong correlation with quantum mechanics")
else:
    print("❌ FAIL: The predictor does not align with quantum entanglement")

# Create visualization
self.plot_results(test_cases, true_metrics, predicted_scores, correlation)

return {
    'correlation': correlation,
    'p_value': p_value,
    'passes_validation': criteria_met,
    'true_metrics': true_metrics,
    'predicted_scores': predicted_scores
}

def plotresults(self, testcases, truemetrics, predictedscores, correlation): """Create visualization of validation results.""" plt.figure(figsize=(12, 8))

# Scatter plot
plt.subplot(2, 2, 1)
plt.scatter(true_metrics, predicted_scores, alpha=0.7, s=60)
plt.plot([0, 1], [0, 1], 'r--', alpha=0.5, label='Perfect Correlation')
plt.xlabel('True Concurrence')
plt.ylabel('Predicted E_AB')
plt.title(f'Correlation: {correlation:.4f}')
plt.legend()
plt.grid(True, alpha=0.3)

# Bar comparison
plt.subplot(2, 2, 2)
x = np.arange(len(test_cases))
width = 0.35
plt.bar(x - width/2, true_metrics, width, label='True Concurrence', alpha=0.7)
plt.bar(x + width/2, predicted_scores, width, label='Predicted E_AB', alpha=0.7)
plt.xlabel('Test Cases')
plt.ylabel('Score')
plt.title('Side-by-Side Comparison')
plt.xticks(x, [tc[:8] for tc in test_cases], rotation=45)
plt.legend()
plt.grid(True, alpha=0.3)

# Residuals
plt.subplot(2, 2, 3)
residuals = np.array(predicted_scores) - np.array(true_metrics)
plt.scatter(true_metrics, residuals, alpha=0.7)
plt.axhline(y=0, color='r', linestyle='--', alpha=0.5)
plt.xlabel('True Concurrence')
plt.ylabel('Residuals (Predicted - True)')
plt.title('Residual Analysis')
plt.grid(True, alpha=0.3)

# Distribution comparison
plt.subplot(2, 2, 4)
plt.hist(true_metrics, bins=10, alpha=0.7, label='True Concurrence', density=True)
plt.hist(predicted_scores, bins=10, alpha=0.7, label='Predicted E_AB', density=True)
plt.xlabel('Score')
plt.ylabel('Density')
plt.title('Distribution Comparison')
plt.legend()
plt.grid(True, alpha=0.3)

plt.tight_layout()
plt.show()

```

def main(): “”“Main execution function.””” validator = QuantumEntanglementValidator() results = validator.runcomprehensivetest()

``` print(f"\n📋 Summary:") print(f"This validation framework tests any claimed entanglement predictor") print(f"against real quantum mechanics. The mock SDKP predictor used here") print(f"fails validation (correlation: {results['correlation']:.4f})") print(f"because it uses non-physical parameters.")

print(f"\n🔬 To test the actual SDKP system:") print(f"Replace 'mocksdkppredictor()' with the real implementation") print(f"and run the same validation protocol.") ```

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