We construct quantum locally testable codes (LTCs) with constant rate, distance, soundness and locality under a variant of a product expansion conjecture of Bafna and Vyas (2026) about Reed-Solomon codes. In particular, we use the high-dimensional expansion framework of Dinur, Lin and Vidick (2024) for constructing quantum LTCs, instantiated with the non-Abelian cubical complexes of Rungtanapirom, Stix, and Vdovina (2019). Our code is obtained by equipping the complex with carefully chosen Reed-Solomon local codes whose symmetries are compatible with those of the complex.