DyLoC: A Dual-Layer Architecture for Secure and Trainable Quantum Machine Learning Under Polynomial-DLA Constraint

Variational quantum circuits face a critical tradeoff between privacy and trainability. High expressivity required for robust privacy induces exponentially large dynamical Lie algebras. This structure inevitably leads to barren plateaus. Conversely, trainable models restricted to polynomial-sized algebras remain transparent to algebraic attacks. To resolve this impasse, DyLoC is proposed. This dual-layer architecture employs an orthogonal decoupling strategy. Trainability is anchored to a polynomial-DLA ansatz while privacy is externalized to the input and output interfaces. Specifically, Truncated Chebyshev Graph Encoding (TCGE) is employed to thwart snapshot inversion. Dynamic Local Scrambling (DLS) is utilized to obfuscate gradients. Experiments demonstrate that DyLoC maintains baseline-level convergence with a final loss of 0.186. It outperforms the baseline by increasing the gradient reconstruction error by 13 orders of magnitude. Furthermore, snapshot inversion attacks are blocked when the reconstruction mean squared error exceeds 2.0. These results confirm that DyLoC effectively establishes a verifiable pathway for secure and trainable quantum machine learning.