Variational quantum algorithms (VQAs) promise near-term quantum advantage, yet parametrized quantum states commonly built from the digital gate-based approach often suffer from scalability issues such as barren plateaus, where the loss landscape becomes flat. We study an analog VQA ansätze composed of $M$ quenches of a disordered Ising chain, whose dynamics is native to several quantum simulation platforms. By tuning the disorder strength we place each quench in either a thermalized phase or a many-body-localized (MBL) phase and analyse (i) the ansätze's expressivity and (ii) the scaling of loss variance. Numerics shows that both phases reach maximal expressivity at large $M$, but barren plateaus emerge at far smaller $M$ in the thermalized phase than in the MBL phase. Exploiting this gap, we propose an MBL initialisation strategy: initialise the ansätze in the MBL regime at intermediate quench $M$, enabling an initial trainability while retaining sufficient expressivity for subsequent optimization. The results link quantum phases of matter and VQA trainability, and provide practical guidelines for scaling analog-hardware VQAs.

翻译：变分量子算法（VQAs）有望在近期实现量子优势，但基于数字门构建的参数化量子态常面临可扩展性问题，如贫瘠高原现象，即损失函数景观变得平坦。我们研究了一种由无序伊辛链的 $M$ 次淬火构成的模拟 VQA 拟设，其动力学过程与多种量子模拟平台原生兼容。通过调节无序强度，我们将每次淬火置于热化相或多体局域化（MBL）相中，并分析（i）拟设的表达能力与（ii）损失函数方差的标度特性。数值模拟表明，两种相在大 $M$ 时均能达到最大表达能力，但热化相中贫瘠高原的出现远早于 MBL 相（即所需 $M$ 值更小）。利用这一差异，我们提出一种 MBL 初始化策略：在中等淬火次数 $M$ 时将拟设初始化为 MBL 状态，从而在保持后续优化所需足够表达能力的同时，获得初始可训练性。该结果建立了物质量子相与 VQA 可训练性之间的关联，并为模拟硬件 VQAs 的规模化提供了实用指导。