quantum-growth-modeling

name

quantum-growth-modeling

description

Quantum growth modeling methodology using parameterized quantum circuits, EWL quantum games, and Dirac-Hamiltonian economic simulation. Applies quantum computing to economic growth, innovation dynamics, capital accumulation, and policy recommendation systems. Use when: analyzing economic growth with quantum methods, modeling innovation ecosystems as quantum systems, implementing quantum game theory for strategic decision-making, simulating capital trajectories with quantum Hamiltonians, building quantum-enhanced recommender systems for policy. Keywords: quantum growth model, Dirac Hamiltonian economics, Solow-Swan quantum, EWL quantum game, innovation ecosystem, capital accumulation quantum, policy recommender quantum, quantum strategic decision, 量子经济增长, 量子哈密顿经济学.

Quantum Growth Modeling

Methodology for modeling economic growth, innovation dynamics, and capital accumulation using quantum computing techniques.

Core Framework

Quantum Game Theory for Economic Modeling

Use Eisert-Wilkens-Lewenstein (EWL) quantum game circuits to model strategic interactions in multi-agent economic systems:

1. Entangle agents: Apply multi-qubit EWL entangler to create superposition of strategies
2. Parameterize local rotations: Each agent's strategy operator is tuned by normalized dominance weights from real data
3. Apply inverse entangler: Collapse entangled state
4. Measure: Measurement probabilities become recommender scores for outcomes

Dirac-Solow-Swan Hamiltonian Integration

Map quantum game outcomes to economic growth simulation:

1. Extract game probabilities: Measurement outcomes from EWL circuit
2. Construct Dirac potential: Map probabilities to diagonal of Dirac Hamiltonian
3. Integrate Solow-Swan dynamics: Combine quantum game outcomes with classical growth model
4. Time-evolve: Simulate capital accumulation and bifurcation dynamics

Implementation Pattern

from qiskit import QuantumCircuit, Aer, execute
import numpy as np

def ewl_quantum_game(weights, n_rounds=1):
    """EWL quantum game circuit parameterized by real economic weights.
    
    Args:
        weights: Normalized dominance weights from real data
        n_rounds: Number of entanglement-measurement rounds
    
    Returns:
        Measurement probabilities as recommender scores
    """
    n = len(weights)
    qc = QuantumCircuit(n)
    
    # EWL Entangler (multi-qubit)
    for i in range(n - 1):
        qc.cx(i, i + 1)
    for i in range(n):
        qc.h(i)
    
    # Parameterized local rotations
    for i, w in enumerate(weights):
        theta = w * np.pi
        qc.ry(theta, i)
    
    # Inverse entangler
    for i in range(n):
        qc.h(i)
    for i in range(n - 2, -1, -1):
        qc.cx(i, i + 1)
    
    # Measure
    qc.measure_all()
    
    backend = Aer.get_backend('qasm_simulator')
    result = execute(qc, backend, shots=1024).result()
    return result.get_counts()

Dirac-Solow-Swan Hamiltonian

def dirac_solow_swan(game_probs, K0, s, delta, n, T=10):
    """Time-evolution of capital under quantum game-influenced dynamics.
    
    Args:
        game_probs: Measurement probabilities from EWL circuit
        K0: Initial capital
        s: Savings rate
        delta: Depreciation rate
        n: Population growth
        T: Time steps
    """
    # Map game probs to Dirac potential (diagonal)
    V = np.diag(np.array(list(game_probs.values())))
    
    # Dirac Hamiltonian: H = alpha.p + beta.m + V
    H = np.zeros((len(V), len(V)))
    for t in range(T):
        K_t = K0 * ((1 - delta) + s * game_probs.get('disruptive', 0.5)) ** t
        # Bifurcation detection
        if abs(K_t - K0 * (1 + n) ** t) > threshold:
            return 'bifurcation', K_t
    return 'stable', K_T

Key Principles

• NISQ-compatible: Circuits with <25 gates and depth <15 are executable on current hardware
• Real data integration: Strategy weights from empirical funding/participation data
• Scaling: Circuit scales as O(n) for n-round helix communications
• Interpretability: Measurement probabilities directly map to policy recommender scores

Activation

Keywords: quantum growth model, Dirac Hamiltonian economics, Solow-Swan quantum, EWL quantum game, innovation ecosystem, capital accumulation, quantum recommender, policy simulation quantum, quadruple helix innovation.