HQFS: Hybrid Quantum Classical Financial Security with VQC Forecasting, QUBO Annealing, and Audit-Ready Post-Quantum Signing

Here’s the corrected paragraph with all punctuation and formatting issues fixed: Financial risk systems usually follow a two-step routine: a model predicts return or risk, and then an optimizer makes a decision such as a portfolio rebalance. In practice, this split can break under real constraints. The prediction model may look good, but the final decision can be unstable when the market shifts, when discrete constraints are added (lot sizes, caps), or when the optimization becomes slow for larger asset sets. Also, regulated settings need a clear audit trail that links each decision to the exact model state and inputs. We present HQFS, a practical hybrid pipeline that connects forecasting, discrete risk optimization, and auditability in one flow. First, HQFS learns next-step return and a volatility proxy using a variational quantum circuit (VQC) with a small classical head. Second, HQFS converts the risk-return objective and constraints into a QUBO and solves it with quantum annealing when available, while keeping a compatible classical QUBO solver as a fallback for deployment. Third, HQFS signs each rebalance output using a post-quantum signature so the allocation can be verified later without trusting the runtime environment. On our market dataset study, HQFS reduces return prediction error by 7.8% and volatility prediction error by 6.1% versus a tuned classical baseline. For the decision layer, HQFS improves out-of-sample Sharpe by 9.4% and lowers maximum drawdown by 11.7%. The QUBO solve stage also cuts average solve time by 28% compared to a mixed-integer baseline under the same constraints, while producing fully traceable, signed allocation records.

💡 Research Summary

The paper introduces HQFS, a hybrid quantum‑classical pipeline that tightly integrates three traditionally separate components of a financial risk management system: (1) forecasting of next‑step returns and volatility using a variational quantum circuit (VQC) combined with a lightweight classical head, (2) conversion of the resulting mean‑variance objective and operational constraints into a Quadratic Unconstrained Binary Optimization (QUBO) problem that can be solved on a quantum annealer or, when hardware is unavailable, on a classical QUBO solver, and (3) a post‑quantum digital signature layer that cryptographically binds each portfolio rebalance decision to the exact model state and timestamp, thereby providing a verifiable audit trail required by regulated environments.

Methodology
The authors first preprocess daily S&P 500 OHLCV data, compute log‑returns and a rolling volatility proxy, and construct normalized feature windows of length L. These windows are encoded into a quantum feature vector by applying a data‑encoding unitary U(X,θ) followed by measurement of observables Oq, yielding differentiable quantum features zq via the parameter‑shift rule. A small classical head fϕ maps z to two scalar predictions: the next‑day return ŕ and volatility σ̂. The joint loss combines mean‑squared error for both targets, weighted by a hyperparameter β, with an ℓ2 regularization term λ to control over‑fitting.

For each rebalance date the predicted expected return vector μ̂ and covariance matrix Σ̂ are assembled. The continuous mean‑variance objective
 min wᵀΣ̂w − η μ̂ᵀw
subject to full‑investment and non‑negativity constraints is discretized by representing each asset weight with B binary bits. A normalization factor Z enforces the budget constraint, and penalty terms ρc penalize any violation of the linear constraints. The resulting QUBO formulation
 min xᵀQx + ρc(aᵀx − 1)²
is compatible with D‑Wave‑style quantum annealers; if an annealer is not accessible, the same QUBO is fed to a classical simulated‑annealing or tabu‑search solver, preserving functional equivalence.

After solving the QUBO, the binary solution x is decoded back into portfolio weights w. A cryptographic hash of the model parameters (θ,ϕ), the decoded weights, and the rebalance timestamp is computed, then signed with a private key sk from a post‑quantum signature scheme (e.g., a lattice‑based scheme). The signed record (t, w, hash, signature) is stored; any auditor can later verify the signature using the public key pk, confirming that the decision originated from the claimed model version at the claimed time.

Experiments
The authors evaluate HQFS on a five‑seed split of the S&P 500 dataset, using a chronological train/validation/test split. Forecasting performance is compared against ARIMA, LSTM, GRU, TCN, and a Transformer encoder. HQFS achieves the lowest MAE and MSE for both return and volatility, and the highest directional accuracy and volatility‑correlation, indicating superior joint prediction quality.

For the allocation stage, baselines include equal‑weight (EW), a classical projected‑gradient mean‑variance optimizer (MV‑PG) using the same μ̂ and Σ̂, and a classical mixed‑integer heuristic (SA‑QUBO) that respects the same binary budget but solves the problem with simulated annealing. HQFS delivers a 9.4 % higher annualized Sharpe ratio, an 11.7 % reduction in maximum drawdown, and a 28 % reduction in average solve time relative to the mixed‑integer baseline, while incorporating realistic transaction costs (10 bps per unit turnover).

Insights and Limitations
The study demonstrates that even modest‑scale VQC embeddings (4–6 qubits, shallow depth) can provide measurable gains over purely classical deep‑learning models when paired with a joint loss that balances return and risk prediction. The QUBO discretization enables the use of quantum annealing to handle combinatorial constraints efficiently; however, solution quality depends on the number of bits per asset (B), and larger B values increase problem size dramatically. The post‑quantum signature adds negligible computational overhead but requires key‑management infrastructure.

Conclusion
HQFS showcases a practical, end‑to‑end quantum‑enhanced financial workflow that improves predictive accuracy, reduces optimization latency, and satisfies regulatory audit requirements through cryptographic signing. By offering a seamless fallback to classical solvers, the pipeline is deployable today while remaining quantum‑ready for future hardware advances. Future work will explore deeper quantum circuits, multi‑objective QUBO formulations, and real‑time verification mechanisms to further close the gap between research prototypes and production‑grade financial systems.