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

Srikumar Nayak

cs.AIFeb 19, 2026

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

Authors: Srikumar Nayak

Organizations: Sr. Member IEEE, Incedo Inc, USA.

Abstract

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.

Figures & tables

Model	$\text{MAE}_{r}\downarrow$	$\text{MSE}_{r}\downarrow$	$\text{DA}_{r}\uparrow$	$\text{MAE}_{\sigma}\downarrow$	$\text{MSE}_{\sigma}\downarrow$	$\text{Corr}(\sigma,\hat{\sigma})\uparrow$
ARIMA [ 6 ]	0.0126 $\pm$ 0.0003	2.31e–4 $\pm$ 0.06e–4	0.521 $\pm$ 0.006	0.0109 $\pm$ 0.0002	1.82e–4 $\pm$ 0.05e–4	0.41 $\pm$ 0.02
LSTM [ 10 ]	0.0118 $\pm$ 0.0003	2.03e–4 $\pm$ 0.05e–4	0.546 $\pm$ 0.007	0.0097 $\pm$ 0.0002	1.55e–4 $\pm$ 0.04e–4	0.52 $\pm$ 0.02
GRU [ 11 ]	0.0116 $\pm$ 0.0002	1.98e–4 $\pm$ 0.05e–4	0.551 $\pm$ 0.006	0.0095 $\pm$ 0.0002	1.51e–4 $\pm$ 0.04e–4	0.54 $\pm$ 0.02
TCN [ 8 ]	0.0114 $\pm$ 0.0002	1.92e–4 $\pm$ 0.04e–4	0.556 $\pm$ 0.006	0.0093 $\pm$ 0.0002	1.47e–4 $\pm$ 0.03e–4	0.56 $\pm$ 0.02
Transformer [ 9 ]	0.0112 $\pm$ 0.0002	1.86e–4 $\pm$ 0.04e–4	0.561 $\pm$ 0.006	0.0091 $\pm$ 0.0002	1.43e–4 $\pm$ 0.03e–4	0.58 $\pm$ 0.02
HQFS	0.0107 $\pm$ 0.0002	1.72e–4 $\pm$ 0.04e–4	0.578 $\pm$ 0.005	0.0086 $\pm$ 0.0002	1.31e–4 $\pm$ 0.03e–4	0.63 $\pm$ 0.02

Table 1: Forecasting results on the test split (mean

\pm

std over

S=5

seeds). Lower is better for MAE/MSE. Best in bold; second best underlined.

Method	AnnRet $\uparrow$	AnnVol $\downarrow$	SR $\uparrow$	MDD $\downarrow$	TO $\downarrow$
Equal-Weight (EW)	0.118 $\pm$ 0.004	0.176 $\pm$ 0.003	0.67 $\pm$ 0.03	0.221 $\pm$ 0.006	0.42 $\pm$ 0.02
MV-PG (forecast inputs)	0.134 $\pm$ 0.005	0.182 $\pm$ 0.004	0.74 $\pm$ 0.03	0.238 $\pm$ 0.007	0.71 $\pm$ 0.03
SA-QUBO (classical)	0.141 $\pm$ 0.004	0.175 $\pm$ 0.003	0.81 $\pm$ 0.03	0.214 $\pm$ 0.006	0.49 $\pm$ 0.02
Transformer + SA-QUBO	0.147 $\pm$ 0.004	0.173 $\pm$ 0.003	0.85 $\pm$ 0.03	0.206 $\pm$ 0.006	0.47 $\pm$ 0.02
HQFS (Ours)	0.156 $\pm$ 0.004	0.171 $\pm$ 0.003	0.91 $\pm$ 0.03	0.192 $\pm$ 0.005	0.44 $\pm$ 0.02

Table 2: Net trading results on the test period (mean

\pm

std over

S=5

seeds). Best in bold; second best underlined.

Setting	$M$	$B$	Time (s) $\downarrow$
SA-QUBO (classical)	30	6	1.42
HQFS QUBO (classical)	30	6	1.05
HQFS QUBO (anneal interface)	30	6	0.62

Table 3: Per-rebalance optimization efficiency (average over test rebalances).

Variant	Corr $(\sigma,\hat{\sigma})$	SR	TO
Classical encoder + MV-PG	0.58	0.74	0.71
Classical encoder + SA-QUBO	0.58	0.85	0.47
VQC encoder + MV-PG	0.63	0.80	0.69
HQFS (VQC + QUBO)	0.63	0.91	0.44

Table 4: Ablation on test (single-seed for clarity).

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Abstract

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