Cut Noise.
Work Quantum.

This paper uses Lie algebras to determine the fundamental limits of how well quantum circuits can approximate functions and provides a new metric to identify training obstacles like barren plateaus.

For quantum machine learning professionals, this work provides a concrete mathematical framework for choosing circuit 'building blocks' that maximize expressive power without sacrificing trainability. The proposed trace-based metric offers a computationally efficient way to screen circuit architectures for barren plateau risks before committing to expensive numerical simulations or hardware runs.