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. 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.

💡 Research Summary

This paper investigates how quantum phases of matter influence the fundamental performance metrics of analog variational quantum algorithms (VQAs). The authors construct an analog ansatz consisting of M global quenches of a disordered transverse‑field Ising chain, a model that is native to several quantum‑simulation platforms (trapped ions, Rydberg arrays, superconducting circuits). By tuning the disorder strength W for each quench, the dynamics can be placed either in a thermalized (ergodic) phase or in a many‑body‑localized (MBL) phase.

Two key properties are examined: (i) expressivity – the ability of the parametrized circuit family to uniformly explore the full Hilbert space, quantified by how closely the ensemble of unitaries generated by the ansatz approximates a unitary 2‑design; and (ii) the scaling of loss‑function variance Var