Some q-supercongruences from squares of basic hypergeometric series

Inspired by the recent work of El Bachraoui and Guo-Li, we establish several q-supercongruences on the truncated forms of squares of basic hypergeometric series modulo the cube and the fourth power of a cyclotomic polynomial. Our proofs heavily rely on the creative microscoping method devised by Guo and Zudilin, a lemma due to El Bachraoui and the Chinese remainder theorem for coprime polynomials.