| 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:
- Entangle agents: Apply multi-qubit EWL entangler to create superposition of strategies
- Parameterize local rotations: Each agent's strategy operator is tuned by normalized dominance weights from real data
- Apply inverse entangler: Collapse entangled state
- Measure: Measurement probabilities become recommender scores for outcomes
Dirac-Solow-Swan Hamiltonian Integration
Map quantum game outcomes to economic growth simulation:
- Extract game probabilities: Measurement outcomes from EWL circuit
- Construct Dirac potential: Map probabilities to diagonal of Dirac Hamiltonian
- Integrate Solow-Swan dynamics: Combine quantum game outcomes with classical growth model
- 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)
for i in range(n - 1):
qc.cx(i, i + 1)
for i in range(n):
qc.h(i)
for i, w in enumerate(weights):
theta = w * np.pi
qc.ry(theta, i)
for i in range(n):
qc.h(i)
for i in range(n - 2, -1, -1):
qc.cx(i, i + 1)
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
"""
V = np.diag(np.array(list(game_probs.values())))
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
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.
