Connecting phases of matter to the flatness of the loss landscape in analog variational quantum algorithms

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. Here we propose an MBL initialization strategy by exploiting this gap: initialize the ansätze in the MBL regime at intermediate quench M, enabling 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.