In this article, taking the quantum Bernstein functions as base functions, we have proposed the class of quantum Bernstein fractal functions. When $f\in 𝒞(I),$the base function is taken as the classical q-Bernstein polynomials, we propose the class of quantum fractal functions through a multivalued quantum fractal operator. When $f\in {ℒ}^p(I),1\le p\le \infty ,$the base function is assumed as q-Kantorovich-Bernstein polynomial to construct the sequence of $(q,\alpha )$-Kantorovich-Bernstein fractal functions that converges uniformly to f. Some approximation properties of these new class of quantum fractal interpolants have been studied.