Quantum-Enhanced Temporal Embeddings via a Hybrid Seq2Seq Architecture

This work investigates how shallow, NISQ-compatible quantum layers can improve temporal representation learning in real-world sequential data. We develop a QLSTM Seq2Seq autoencoder in which a depth-1 variational quantum circuit is embedded inside each recurrent gate, shaping the geometry of the learned latent manifold. Evaluated on fourteen rolling S and P 500 windows from 2022 to 2025, the quantum-enhanced encoder produces smoother trajectories, clearer regime transitions, and more stable, sector-coherent clusters than a classical LSTM baseline. These geometric properties support the use of a Radial Basis Function (RBF) kernel for downstream portfolio allocation, where both RBF-Graph and RBF-DivMom strategies consistently outperform their classical counterparts in risk-adjusted terms. Analysis across periods shows that compressed manifolds favor concentrated allocation, while dispersed manifolds favor diversification, demonstrating that latent geometry serves as a regime indicator. The results highlight a practical role for shallow hybrid quantum and classical layers in NISQ-era sequence modeling, offering a reproducible pathway for improving temporal embeddings in finance and other data-limited, noise-sensitive domains.