Reliable preparation of many-body ground states is an essential task in quantum computing, with applications spanning areas from chemistry and materials modeling to quantum optimization and benchmarking. A variety of approaches have been proposed to tackle this problem, including variational methods. However, variational training often struggle to navigate complex energy landscapes, frequently encountering suboptimal local minima or suffering from barren plateaus. In this work, we introduce an iterative strategy for ground-state preparation based on a stepwise (discretized) Hamiltonian deformation. By complementing the Variational Quantum Eigensolver (VQE) with adiabatic principles, we demonstrate that solving a sequence of intermediate problems facilitates tracking the ground-state manifold toward the target system, even as we scale the system size. We provide a rigorous theoretical foundation for this approach, proving a lower bound on the loss variance that suggests trainability throughout the deformation, provided the system remains away from gap closings. Numerical simulations, including the effects of shot noise, confirm that this path-dependent tracking consistently converges to the target ground state.

翻译：可靠制备多体基态是量子计算中的一项基本任务，其应用范围涵盖化学与材料建模、量子优化及基准测试等多个领域。针对该问题已提出多种方法，包括变分方法。然而，变分训练往往难以驾驭复杂的能量景观，常陷入次优局部极小值或遭遇贫瘠高原问题。本研究提出一种基于逐步（离散化）哈密顿量形变的迭代式基态制备策略。通过将变分量子本征求解器（VQE）与绝热原理相结合，我们证明即使扩大系统规模，求解一系列中间问题仍能有效追踪基态流形直至目标系统。我们为此方法建立了严格的理论基础，证明了损失方差的下界，表明只要系统远离能隙闭合点，在整个形变过程中均可保持可训练性。包含散粒噪声效应的数值模拟证实，这种路径依赖的追踪方法能稳定收敛至目标基态。