Adaptive H-EFT-VA: A Provably Safe Trajectory Through the Trainability-Expressibility Landscape of Variational Quantum Algorithms
For quantum machine learning practitioners, this provides the first provably safe trajectory through the trainability-expressibility tradeoff, eliminating hyperparameter search and enabling deployment on near-term quantum devices.
Adaptive H-EFT-VA (A-H-EFT) solves the Barren Plateau problem in variational quantum algorithms by safely expanding the reachable Hilbert space along a trajectory, achieving fidelity F=0.54 (doubling static H-EFT-VA's 0.27) and outperforming HEA (F~0.01) on 16 experiments up to N=14, with gradient variance >= 0.5 throughout.
H-EFT-VA established a physics-informed solution to the Barren Plateau (BP) problem via a hierarchical EFT UV-cutoff, guaranteeing gradient variance in Omega(1/poly(N)). However, localization restricts the ansatz to a polynomial subspace, creating a reference-state gap for states distant from |0>^N. We introduce Adaptive H-EFT-VA (A-H-EFT) to navigate the trainability-expressibility tradeoff by expanding the reachable Hilbert space along a safe trajectory. Gradient variance is maintained in Omega(1/poly(N)) if sigma(t) <= 0.5/sqrt(LN) (Theorem 1). A Safe Expansion Corollary and Monotone Growth Lemma confirm expansion without discontinuous jumps. Benchmarking across 16 experiments (up to N=14) shows A-H-EFT achieves fidelity F=0.54, doubling static H-EFT-VA (F=0.27) and outperforming HEA (F~0.01), with gradient variance >= 0.5 throughout. For Heisenberg XXZ (Delta_ref=1), A-H-EFT identifies the negative ground state while static methods fail. Results are statistically significant (p < 10^-37). Robustness over three decades of hyperparameters enables deployment without search. This is the first rigorously bounded trajectory through the VQA landscape.