Adaptive H-EFT-VA: A Provably Safe Trajectory Through the Trainability-Expressibility Landscape of Variational Quantum Algorithms

TL;DR

This paper introduces Adaptive H-EFT-VA, a method that safely navigates the tradeoff between trainability and expressibility in variational quantum algorithms, achieving higher fidelity and robustness in experiments.

Contribution

The authors propose A-H-EFT-VA, a novel approach that expands the Hilbert space along a safe trajectory, with proven bounds and superior experimental performance over static methods.

Findings

A-H-EFT-VA maintains gradient variance Omega(1/poly(N)) during expansion.

A-H-EFT-VA doubles fidelity compared to static H-EFT-VA in benchmarks.

A-H-EFT-VA successfully identifies the negative ground state in Heisenberg XXZ model.

Abstract

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.