用量子物态调控模拟型变分量子算法的训练难度。
Connecting phases of matter to the flatness of the loss landscape in analog variational quantum algorithms
- 通过调节无序强度，让每次演化处于热化或多体局域相。
- 多体局域相在更少演化次数下仍保持可训练性，避免梯度消失。
- 提出基于多体局域相的初始化策略，适合硬件原生模拟型量子算法。
变分量子算法（VQA）有望实现近期量子优势，但基于数字门的参数化量子态常因可扩展性问题导致梯度消失（即平坦损失景观）。本文研究一种由 $M$ 次无序伊辛链淬火构成的模拟型 VQA 电路，其动力学天然适配多种量子模拟平台。通过调节无序强度，将每次淬火置于热化相或多体局域（MBL）相，并分析 (i) 电路的表达能力与 (ii) 损失方差的缩放行为。数值结果显示，两种相在 $M$ 较大时均达到最大表达力，但热化相在远小的 $M$ 下即出现梯度消失，而 MBL 相则延迟该现象。利用此差异，提出一种基于 MBL 的初始化策略：在中等 $M$ 时从 MBL 区域初始化，既保证初始可训练性，又保留后续优化所需的表达能力。结果揭示了量子物态与 VQA 可训练性的联系，为模拟型硬件上 VQA 的可扩展性提供了实用指导。
原文摘要 · Abstract (English)
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.
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