trapped-ion-portfolio-optimization

# Trapped-Ion Portfolio Optimization ## Core Concept End-to-end pipeline that decomposes large portfolio optimization problems into hardware-embeddable QUBO subproblems, solves them on trapped-ion quantum processors using BF-DCQO (Bias-Field Digitized Counterdiabatic Quantum Optimization), and recombines solutions with cardinality-preserving post-processing. ## Workflow ### Phase 1: Correlation Analysis 1. **RMT-based Denoising**: Apply Random Matrix Theory to clean the correlation matrix - Compute eigenvalue spectrum of asset return correlations - Filter eigenvalues within the Marcenko-Pastur bulk (noise) - Reconstruct denoised correlation matrix from significant eigenvalues only 2. **Community Detection**: Identify groups of correlated assets - Apply Louvain or similar community detection on the correlation graph - Each community becomes a candidate subproblem ### Phase 2: QUBO Decomposition 3. **Correlation-Guided Greedy Splitting**: Cap each cluster by executable qubit budget ``` For each community C: if |C| <= qubit_budget: subproblem = C else: split C into chunks of size <= qubit_budget using correlation-guided greedy partitioning ``` 4. **BF-DCQO Execution**: Solve each subproblem non-variationally - No classical parameter-training loops (avoids barren plateaus) - Uses counterdiabatic driving terms for faster convergence - Bias fields steer optimization toward feasible solutions ### Phase 3: Recombination and Post-Processing 5. **Candidate Recombination**: Merge low-energy candidates into global portfolios 6. **Two-Stage Post-Processing**: - **Fast Repair**: Fix constraint violations (budget, cardinality) - **Cardinality-Preserving Swap Local Search**: Optimize within fixed cardinality ## Key Parameters | Parameter | Typical Value | Description | |-----------|--------------|-------------| | Qubit Budget | 20-64 | Max qubits per subproblem (hardware-dependent) | | Universe Size | 100-500 | Total assets in portfolio | | Cardinality K | 10-50 | Number of assets to select | ## Pattern: Hardware-Aware Problem Decomposition When NISQ devices have limited qubits: 1. Cluster the problem using domain knowledge (correlations) 2. Split clusters to fit hardware constraints 3. Solve subproblems independently 4. Recombine with feasibility-preserving operations ## Benchmarks - Demonstrated on 250-asset S&P 500 universe - Executed on 64-qubit Barium development system (IonQ Tempo line) - Larger executable subproblems → reduced decomposition error → better risk-return trade-offs ## Pitfalls - **Decomposition error**: Splitting loses cross-cluster correlations - **Hardware noise**: NISQ errors accumulate with circuit depth - **Post-processing bottleneck**: Repair step may degrade quantum advantage - **Turnover**: High portfolio turnover increases transaction costs ## References - arXiv: 2602.23976 - "Large-scale portfolio optimization on a trapped-ion quantum computer"