Quantum advantage versus barren plateaus for polynomial and exponential dynamical Lie algebras

Determine whether quantum advantage remains when using ansatzes whose dynamical Lie algebras have polynomial dimension, and establish whether exponentially scaling dynamical Lie algebras necessarily induce barren plateaus that are detrimental to machine-learning applications.

Background

The paper contrasts ansatzes with polynomially sized dynamical Lie algebras, which can be efficiently simulated classically, with ansatzes having exponentially scaling dynamical Lie algebras. The former raise the unresolved issue of whether any quantum advantage remains, while the latter are associated with a conjectured risk of barren plateaus and consequent training difficulties.

References

Certain ansatzes generate polynomial sized DLA, although their existence raises an important question: if there remains quantum advantage in using such ansatzes as techniques exist that can efficiently simulate such polynomial DLA circuits on classical hardware . So one can return to an exponentially scaling DLA to resolve the quantum advantage question, whereby another dilemma is revealed as it has been conjectured that an exponential DLA can induce barren plateaus in turn becoming detrimental for machine learning applications .

— Subspace Controllability in Variational Quantum Circuits: Maximising Expressivity and Increasing Search Efficiency with Dynamical Lie Algebras  (2609.24475 - Barlow et al., 21 Sep 2026) in Section 2.2, “Controllability of the hardware efficient ansatz”