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

Understand

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 ans\"atze 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 ans\"atze'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.