Some q-supercongruences from the Gasper and Rahman quadratic summation

We give four families of q-supercongruences modulo the square and cube of a cyclotomic polynomial from Gasper and Rahman's quadratic summation. As conclusions, we obtain four new supercongruences modulo p(2) or p(3), such as: for d >= 2, r >= 1 with gcd(d, r) = 1 and d + r odd, and any prime p equivalent to d + r (mod 2d) with p >= d + r, Sigma(p-1)(k=0)(3dk + r) (r/d)(d-r/d)k(r/2d)(k)(2)(1/2)k/k!(4)(d+2r/2d)k equivalent to 0 (mod p(3)), where (x)(n) = x(x + 1) . . . (x + n - 1) is the Pochhammer symbol. We also propose three related conjectures on q-supercongruences.