certified-higher-order-qaoa-collateral

# Certified Higher-Order QAOA for Collateral Optimization ## Core Concept CR-HO-QAOA: A certified higher-order quantum framework for margin- and CSA-aware collateral allocation in uncleared derivatives. Institutions must satisfy margin requirements while respecting CSA eligibility rules, valuation percentages, rounding, transfer thresholds, concentration limits, custody conditions, inventory, and VM/IM/IA side constraints. The framework maps higher-order binary models into Pauli-Z cost Hamiltonians and uses **collateral-specific feasible-subspace mixers** to preserve one-hot choices, movement budgets, and side assignments. Candidates are decoded, repaired if needed, evaluated under an eight-term production objective, and **certified by a deterministic CP-SAT master solver** before any recommendation is reported. ## Architecture ### Adapter-First Margin Normalization - Official SIMM, proxy SIMM, legacy IA, VM-only, RQV, or hybrid margin sources normalized into common `MarginRequirement` - Optimizer does NOT calculate or replace official SIMM — acts as adapter layer ### Higher-Order Binary Model - Hyperedges capture: concentration pressure, custody batches, substitution tickets, chunky lots, liquidity effects, overshoot, side-specific requirements - Goes beyond QUBO to capture multi-variable interactions natively ### Quantum Layer - Maps hyperedges into Pauli-Z cost Hamiltonian - Feasible-subspace mixers preserve structural constraints (one-hot, movement budgets, side assignments, substitution structure) - Improves certified sample quality vs. QUBO-style and generic-mixer baselines ### CP-SAT Certification - Deterministic CP-SAT master solver acts as feasibility and governance arbiter - Every quantum candidate must pass certification before being reported - Quantum layer generates candidates; classical solver certifies ## Workflow ### Step 1: Margin Requirement Normalization 1. Collect margin requirements from all sources (SIMM, proxy SIMM, legacy IA, VM-only, RQV) 2. Normalize into common MarginRequirement structure 3. Load CSA terms and current inventory ### Step 2: Build Active Neighborhood 1. Define bounded set of actions: pledge, recall, substitution, batch, slack 2. Identify hyperedges: concentration pressure, custody batches, substitution tickets, chunky lots, liquidity effects, overshoot, side-specific requirements 3. Construct higher-order binary optimization model ### Step 3: Quantum Optimization 1. Map hyperedges to Pauli-Z cost Hamiltonian 2. Apply collateral-specific feasible-subspace mixers 3. Run quantum circuit to generate candidate solutions 4. Decode candidates, repair constraint violations if needed ### Step 4: CP-SAT Certification 1. Evaluate candidates under eight-term production objective 2. Pass candidates through deterministic CP-SAT master solver 3. Only certified recommendations are reported ### Step 5: Output - Certified optimal or near-optimal collateral allocation - Feasibility guarantee from CP-SAT arbiter ## Key Advantages vs Standard QAOA | Aspect | Standard QAOA | CR-HO-QAOA | |--------|---------------|------------| | Constraint model | QUBO (quadratic only) | Higher-order binary (k-body terms) | | Mixer | Generic transverse-field | Feasible-subspace (preserves structure) | | Certification | None | CP-SAT deterministic solver | | Constraint handling | Penalty-based | Feasible-subspace + repair | | Applicability | Generic optimization | Domain-specific (collateral/finance) | ## Error Handling ### Quantum Candidate Infeasible - Apply repair heuristics to fix constraint violations - Re-evaluate under production objective - If still infeasible, discard and generate next candidate ### CP-SAT Timeout - Use best certified candidate found so far - Report uncertainty level with recommendation - Fall back to classical optimization if no certified candidates ### No Quantum Advantage - Framework designed as hybrid: quantum generates candidates, classical certifies - Even without quantum advantage, higher-order modeling provides value over QUBO - CP-SAT serves as baseline and governance arbiter ## Activation Keywords - certified QAOA collateral - margin-aware quantum optimization - CSA collateral allocation - higher-order QAOA finance - feasible-subspace mixer - quantum collateral optimization - CP-SAT quantum certification - 保证金优化量子 - 担保品分配量子 - higher-order binary optimization finance ## Resources - arXiv:2606.04235 — A Certified Higher Order Quantum Framework for CSA and Margin-Aware Collateral Optimization ## Related Skills - higher-order-portfolio-qaoa - quantum-portfolio-optimizer - constraint-preserving-quantum-mixers - quantum-finance-portfolio