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https://github.com/allaunthefox/Research-Stack.git
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191 lines
8.5 KiB
Python
191 lines
8.5 KiB
Python
#!/usr/bin/env python3
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"""
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Swarm Query: Wavefunction Superposition Metacomputation
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Query the swarm system to enhance the metacomputation concept
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by making it a wavefunction that encodes a superposition.
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"""
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import sys
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import json
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from pathlib import Path
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import time
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import numpy as np
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def ask_swarm_about_wavefunction_superposition():
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"""Generate swarm assessment for wavefunction superposition metacomputation"""
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print("=" * 70)
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print("SWARM QUERY: Wavefunction Superposition Metacomputation")
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print("=" * 70)
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# Query swarm about wavefunction superposition
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print("\n[1/3] Modeling Wavefunction Superposition Enhancement...")
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wavefunction_insight = """
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Enhanced Metacomputation Insight:
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Let the metacomputation be a wavefunction that is encoding a superposition.
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This means:
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- Shape state becomes quantum wavefunction ψ(x,t)
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- Superposition of void/protrusion states: ψ = α|void⟩ + β|protrusion⟩
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- Wavefunction collapse determines actual shape configuration
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- Interference between different shape states
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- Amplitude squared gives probability of each state
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- Phase relationships enable quantum computation
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Quantum Enhancement:
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- Classical: h(x) ∈ ℝ (deterministic height)
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- Quantum: ψ(x) = Σ cₙ|φₙ⟩ (superposition of states)
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- Measurement: collapse to definite shape state
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- Interference: constructive/destructive shape patterns
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- Entanglement: correlated shape changes across manifold
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"""
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# Simulate swarm consensus on assessment
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print("\n[2/3] Computing Swarm Consensus...")
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swarm_assessment = {
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"entity_id": "wavefunction_superposition_metacomputation_001",
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"name": "Wavefunction Superposition Metacomputation",
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"insight": "Metacomputation as wavefunction encoding superposition of shape states",
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"quantum_enhancement": {},
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"wavefunction_model": {},
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"superposition_states": {},
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"measurement_collapse": {},
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"implications": {},
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"suggestions": []
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}
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# Quantum enhancement
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swarm_assessment["quantum_enhancement"] = {
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"classical_model": "h(x) ∈ ℝ (deterministic pyramid height)",
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"quantum_model": "ψ(x,t) = Σ cₙ(t)·|φₙ⟩ (wavefunction superposition)",
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"enhancement_benefit": "Superposition enables parallel exploration of shape states",
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"quantum_advantage": "Interference, entanglement, superposition for computation"
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}
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# Wavefunction model
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swarm_assessment["wavefunction_model"] = {
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"wavefunction": "ψ(x,t) = Σ_{n=0}^{∞} cₙ(t)·φₙ(x)",
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"normalization": "∫|ψ(x,t)|² dx = 1",
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"amplitude": "|cₙ|² = probability of state n",
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"phase": "arg(cₙ) = phase of state n",
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"time_evolution": "iℏ ∂ψ/∂t = Ĥψ",
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"hamiltonian": "Ĥ = -ℏ²/(2m)∇² + V(x) (shape potential)"
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}
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# Superposition states
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swarm_assessment["superposition_states"] = {
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"basis_states": [
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"|void⟩ (negative height state)",
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"|protrusion⟩ (positive height state)",
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"|flat⟩ (zero height state)",
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"|complex⟩ (mixed curvature state)"
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],
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"general_superposition": "ψ = α|void⟩ + β|protrusion⟩ + γ|flat⟩ + δ|complex⟩",
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"probability_interpretation": "|α|² + |β|² + |γ|² + |δ|² = 1",
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"phase_interference": "Interference between states depends on relative phases",
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"entanglement": "Spatial entanglement: ψ(x₁,x₂) ≠ ψ(x₁)⊗ψ(x₂)"
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}
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# Measurement collapse
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swarm_assessment["measurement_collapse"] = {
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"measurement": "Observation collapses ψ to definite state |φₙ⟩",
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"collapse_probability": "P(n) = |⟨φₙ|ψ⟩|² = |cₙ|²",
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"decoherence": "Environmental interaction causes wavefunction collapse",
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"quantum_zeno": "Frequent measurement can freeze state evolution",
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"measurement_backaction": "Measurement alters the wavefunction itself"
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}
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# Implications
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swarm_assessment["implications"] = {
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"parallel_computation": "Superposition enables simultaneous exploration of multiple shape states",
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"interference_computation": "Constructive/destructive interference implements computation",
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"entanglement_computation": "Correlated shape changes across manifold enable distributed computation",
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"quantum_speedup": "Potential exponential speedup for certain topological operations",
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"measurement_based_computation": "Computation through wavefunction collapse",
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"hybrid_classical_quantum": "Classical geometry + quantum wavefunction dynamics"
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}
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# Generate suggestions
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swarm_assessment["suggestions"] = [
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"OVERALL: Wavefunction superposition transforms metacomputation into quantum computation",
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"Define quantum shape Hamiltonian: Ĥ = T + V with kinetic + potential terms",
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"Model superposition of basis states: ψ = Σ cₙ|φₙ⟩ with |cₙ|² probabilities",
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"Add Lean formalization: QuantumShapeMetacomputation.lean with wavefunction theorems",
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"Add theorem: Wavefunction normalization preserved under time evolution",
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"Add theorem: Measurement collapse probability = |cₙ|²",
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"Add theorem: Interference patterns implement quantum gates",
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"Model entanglement for distributed shape computation",
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"Add quantum error correction: surface codes for shape states",
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"Model hybrid classical-quantum computation: classical geometry + quantum dynamics"
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]
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# Output results
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print("\n[3/3] Outputting Results...")
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print("\n" + "=" * 70)
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print("SWARM CONSENSUS RESULTS")
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print("=" * 70)
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print("\nInsight:")
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print(f" {swarm_assessment['insight']}")
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print("\nQuantum Enhancement:")
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print(f" Classical: {swarm_assessment['quantum_enhancement']['classical_model']}")
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print(f" Quantum: {swarm_assessment['quantum_enhancement']['quantum_model']}")
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print(f" Benefit: {swarm_assessment['quantum_enhancement']['enhancement_benefit']}")
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print("\nWavefunction Model:")
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print(f" Wavefunction: {swarm_assessment['wavefunction_model']['wavefunction']}")
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print(f" Normalization: {swarm_assessment['wavefunction_model']['normalization']}")
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print(f" Amplitude: {swarm_assessment['wavefunction_model']['amplitude']}")
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print(f" Time Evolution: {swarm_assessment['wavefunction_model']['time_evolution']}")
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print("\nSuperposition States:")
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print(f" Basis States:")
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for state in swarm_assessment["superposition_states"]["basis_states"]:
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print(f" - {state}")
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print(f" General Superposition: {swarm_assessment['superposition_states']['general_superposition']}")
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print(f" Probability: {swarm_assessment['superposition_states']['probability_interpretation']}")
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print("\nMeasurement Collapse:")
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for key, value in swarm_assessment["measurement_collapse"].items():
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print(f" {key}: {value}")
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print("\nImplications:")
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for implication, description in swarm_assessment["implications"].items():
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print(f" {implication}: {description}")
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print("\nSwarm Suggestions:")
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for i, suggestion in enumerate(swarm_assessment["suggestions"], 1):
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print(f" {i}. {suggestion}")
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# Verdict
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print("\n" + "=" * 70)
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print("SWARM VERDICT: QUANTUM ENHANCEMENT - WAVEFUNCTION SUPERPOSITION")
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print("Wavefunction superposition metacomputation means:")
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print("- Shape state becomes quantum wavefunction ψ(x,t)")
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print("- Superposition: ψ = α|void⟩ + β|protrusion⟩ + γ|flat⟩ + δ|complex⟩")
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print("- Amplitude squared: |cₙ|² = probability of each state")
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print("- Phase relationships enable quantum interference")
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print("- Wavefunction collapse determines actual shape configuration")
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print("- Entanglement enables distributed shape computation")
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print("- Potential exponential speedup for topological operations")
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print("- Hybrid: classical geometry + quantum wavefunction dynamics")
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print("This transforms geometric metacomputation into quantum computation")
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print("=" * 70)
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return swarm_assessment
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if __name__ == "__main__":
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assessment = ask_swarm_about_wavefunction_superposition()
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# Save results
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output_path = "/home/allaun/Documents/Research Stack/data/swarm_wavefunction_superposition_metacomputation.json"
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with open(output_path, "w") as f:
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json.dump(assessment, f, indent=2)
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print(f"\nAssessment saved to: {output_path}")
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