Quantum Hyperbolic Deep Learning for Foreign-Exchange Trading: A Hybrid Reinforcement-Learning Pipeline over Attractor-Aware Magnet-Price Manifolds

Foreign-exchange decisions rest on hierarchically organized evidence whose latent structure is inadequately captured by Euclidean representations. Reinforcement-learning agents trained on flat embeddings inherit stability guarantees that do not transfer to the manifold supporting the latent state. We address both limitations through a hybrid architecture in which a schema-constrained structured chain-of-thought is embedded into a Poincaré ball, transported to a qubit register via angle encoding, and processed by an L-layer hardware-efficient variational ansatz on a state-vector backend. The circuit exposes two read-outs to the policy, namely, a scalar Pauli-Z observable and a projected quantum kernel inducing a fidelity-based similarity over magnet-price attractors, the latter identified via kernel-weighted recurrence density and finite-time Lyapunov statistics. The Lipschitz constraint on the action-value function is lifted from the hyperbolic geodesic distance to a joint metric on Bκn×P(H). A stability theorem yields an explicit bound depending on the read-out operator norm, on the depth–width product of the ansatz, and on the curvature–Hilbert balance. The pipeline is evaluated on nine major FX crosses over a 2015–2025 out-of-sample window, with rolling-origin walk-forward retraining and broker-published transaction costs. The system attains 2.55% pair-averaged non-compounded monthly P&L and 8.83% maximum drawdown, with Sharpe 1.78, Calmar 3.43, and Probabilistic Sharpe Ratio exceeding 0.95 on every cross. The gain remains significant under a deflated-Sharpe-ratio test with Ntrials=42 correction. Block-wise ablations exhibit strictly monotone degradation: removing the projected kernel costs −4.15 p.p. on annualized P&L, the joint Lipschitz penalty −6.42 p.p., the attractor module −7.64 p.p., and the hyperbolic embedding −8.40 p.p. The quantum block thereby instantiates a structurally non-classical, geometry-aware regularizer identifiable through ablation rather than asymptotically advantageous.