A 13-qubit quantum optimization pipeline for constrained portfolio selection, implementing a novel Relational Information Theory (RIT) penalty framework for QUBO formulation.
Select K=4 assets from an 8-stock universe (NVDA, MSFT, LLY, XOM, JNJ, PG, JPM, BRK-B) to minimize portfolio variance while maximizing returns, subject to:
- Cardinality constraint: Exactly 4 assets
- Budget constraint: Normalized cost ≤ B' = 1.638
- Sector caps: ≤2 assets per sector
| Phase | Description | Key Output |
|---|---|---|
| Phase 1 | Market data retrieval, covariance estimation, QUBO formulation | 8×8 covariance matrix, penalty coefficients |
| Phase 2 | Classical baseline (brute force, greedy, continuous relaxation) | Optimal portfolio: {NVDA, JNJ, PG, JPM} |
| Phase 3 | QUBO validation, Ising mapping, spectral analysis | 13×13 QUBO matrix, ground state E* = -0.6156 |
| Phase 4 | QAOA with CVaR objective, multi-start Powell optimization | Quantum solution recovery |
Penalty coefficients derived from information-theoretic principles:
- α₁ (cardinality) = 0.036058 (sufficiency floor × 1.05 safety margin)
- α₂ (budget) = 0.007356 (peer condition)
| Method | Portfolio | Objective | Runtime |
|---|---|---|---|
| Brute Force (exact) | NVDA, JNJ, PG, JPM | -0.018961 | 0.1s |
| Greedy | NVDA, JNJ, PG, JPM | -0.018961 | <0.1s |
| QAOA p=5 | NVDA, JNJ, PG, JPM | -0.018961 | 45s |
| Depth (p) | ⟨H⟩ Energy | P(ground state) | Target Match |
|---|---|---|---|
| 1 | -0.491 | 0.000122 | ✗ |
| 3 | -0.543 | 0.000456 | ✗ |
| 5 | -0.598 | 0.002341 | ✓ |
| 8 | -0.612 | 0.008912 | ✓ |