Trainability paths on barren plateau landscapes

Determine whether, in barren plateau loss landscapes arising in variational quantum circuits, optimization trajectories from realistic initializations to reasonable problem solutions with sufficiently large gradients exist and can be practically identified to enable training.

Background

The paper reviews the barren plateau phenomenon, where loss landscapes of variational quantum algorithms exhibit exponentially concentrated values, leading to vanishing gradients for most parameter choices as problem size grows. This makes gradient-based training require exponentially many shots in typical unstructured settings.

The authors emphasize that barren plateaus are an average-case notion: practitioners care about trajectories from initializations to solutions rather than random points. They note that trainable paths with non-vanishing gradients could, in principle, exist even when the landscape is largely flat, but whether these can be found in practice is unresolved.

References

It remains an open question whether or not such trajectories can be found in practice.

— Myths around quantum computation before full fault tolerance: What no-go theorems rule out and what they don't  (2501.05694 - Zimborás et al., 10 Jan 2025) in Subsection 'Variational quantum algorithms', Subsubsection 'Fundamental limitations of variational quantum algorithms'

Understanding why a covariance-adapting search locates and remains within the atypical regions identified here, and whether that behaviour persists as $n$ grows, is the open question this work raises most directly.

— Variational Quantum Linear Solver via Block Encoding for the Poisson Equation  (2608.19655 - Dsouza et al., 20 Aug 2026) in Section 5, Conclusion and Future Work