⚛️ Quantum-Inspired Optimization
QUBO formulation with QAOA simulation and classical solver comparison
🔧 Optimization Parameters
%
📐 QUBO Formulation
min xTQx
The inventory problem is encoded as a Quadratic Unconstrained Binary Optimization:
Holding CostΣ
h·q·2iCost of storing excess inventory
Ordering CostK
· δ(q > 0)Fixed cost per order placed
Stockout Costp
· max(0, D - I)Penalty for unmet demand
Constraintλ(Σ
xi·2i - Q*)2Service
level penalty term
⚡ QAOA Circuit
|ψ(γ,β)⟩ =
UM(βp)UC(γp)...|+⟩⊗n
Cost Unitary
UC(γ) = e-iγC applies problem structure
Mixer Unitary
UM(β) = e-iβB explores solution space
Measurement
Sample bit-strings, decode to order quantities
📈 QAOA Convergence
🌊 QUBO Energy Landscape
🔬 Solver Comparison
| Solver | Energy | Solution | Time | Why This Works |
|---|---|---|---|---|
| 🎯 Exact (Brute Force) | -42.50 | Q=85 | 12.4s | Guaranteed optimal, O(2n) complexity |
| ⚛️ QAOA (p=3) | -42.31 | Q=83 | 1.8s | Variational quantum eigensolver approximation |
| 🔥 Simulated Annealing | -41.82 | Q=81 | 0.3s | Metropolis criterion escapes local minima |
| 📋 Tabu Search | -40.15 | Q=78 | 0.2s | Memory-based search avoids revisiting |
| 🎲 Random Search | -38.52 | Q=72 | 0.1s | Baseline - no intelligent exploration |
✅ Optimal Decision
85Order
Quantity
127Reorder Point
$2,340Total Cost
96.2%Service Level