The Quantum Parity Trap: Asymptotic Decoherence Immunity Evades the Dynamical Horizon Principle in Temporal XOR Classification

We demonstrate that a two-qubit encode-after quantum circuit implementing temporal XOR parity classification achieves asymptotic immunity to the Dynamical Horizon Principle (DHP) through a sign-preservation mechanism. The DHP, an empirically observed characterization related to the classical vanishing gradient problem, predicts training failure when the convergence time T_conv exceeds 0.72 times the Lyapunov coherence time τ_L. We show that for even convergence steps, the Bloch sphere contraction factor (1−4p/3)^T_conv remains strictly positive for all Pauli depolarizing rates p ∈ [0, 0.75), ensuring gradient direction is preserved regardless of noise magnitude. We term this the quantum parity trap: a regime where the optimizer receives consistent directional signal even as coherence approaches zero. Threshold sweeps confirm convergence at T_conv/τ_L ratios exceeding 15×, compared to the classical DHP limit of 0.72×—a quantum advantage that diverges as p → 0.75. Supplementary experiments establish that (1) Rigetti QPU hardware yields >50σ margin above chance with 4096 shots and readout error mitigation; (2) gradient direction alone is sufficient for convergence—signSGD matches Adam while vanilla SGD fails; and (3) T1 amplitude damping does not replicate the landscape regularization effect of Pauli depolarizing noise, revealing that isotropic Bloch sphere contraction is the mechanistic source of partial-attractor erasure. These results demonstrate that task structure, channel geometry, and optimizer design jointly determine whether quantum noise enables or impedes machine learning convergence.