Comment on "Provably Trainable Rotationally Equivariant Quantum Machine Learning"

Abstract

We comment on the article by West {et al.}, ``Provably Trainable Rotationally Equivariant Quantum Machine Learning'' [PRX Quantum , 030320 (2024)]. While the general framework is insightful, we identify a key inconsistency in the construction of the dynamical Lie algebra (DLA). Specifically, the fixed controlled-Z (CZ) gates applied to all nearest-neighbor qubits are treated as if they were parameterized gates, with generators expressed in terms of combinations of Pauli operators. We discuss the implications of this inclusion and encourage the authors to revisit their analysis using a corrected DLA formulation.