Quantum-Assisted Recommender Algorithms for Financial Asset Recommendation: Theoretical Bounds and Empircal Validation

Abstract We present a unified, practical pipeline for a quantum-assisted financial recommender system. Investor similarity graphs are constructed from high-dimensional profiles, compressed via normalized Laplacian spectral embedding, and optimized using the Quantum Approximate Optimization Algorithm (QAOA) on GPU-based quantum simulators (cuQuantum, Cirq-GPU, Cirq with IonQ simulation). We consolidate theoretical derivations (QUBO/Ising mapping, spectral compression correctness, QAOA parameter optimization) and implementation details (feature selection, Nyström extension, QAOA parameter optimization). The key contribution is a unified theoretical framework that directly connects QAOA optimization to classification performance, eliminating disjoint post-processing steps. We provide complete, rigorous proofs of all error bounds, including a variance bound for QAOA concentration, an explicit treatment of the degree-matrix discrepancy, unbalanced misclassification, effective VC dimension, and the QAOA approximation ratio. Two explicit caveats are documented: (i) the overcomplete feature regime is rank-deficient, with generalization controlled solely by the downstream bottleneck and dropout; and (ii) the unconstrained PAC bound is vacuous for target accuracies above roughly (15%), which formally motivates the Laplacian-constrained effective VC dimension. Results show that spectral compression enables tractable quantum optimization for mid-sized problems and that Cirq-GPU offers a favorable speed-accuracy trade-off. We discuss deployment considerations for financial institutions, including explainability, compliance, and workflows under the likely hybrid classical-quantum architecture. Mathematics Subject Classification (2020) 68Q12 · 81P68 · 91G10 · 68T05 · 90C27