Adaptive H-EFT-VA: A Provably Safe Trajectory Through the Trainability-Expressibility Landscape of Variational Quantum Algorithms
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914466882387968 |
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| author | Hamid, Eyad I. B. |
| author_facet | Hamid, Eyad I. B. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_10607 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adaptive H-EFT-VA: A Provably Safe Trajectory Through the Trainability-Expressibility Landscape of Variational Quantum Algorithms Hamid, Eyad I. B. Quantum Physics Machine Learning High Energy Physics - Theory 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. |
| title | Adaptive H-EFT-VA: A Provably Safe Trajectory Through the Trainability-Expressibility Landscape of Variational Quantum Algorithms |
| topic | Quantum Physics Machine Learning High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.10607 |