Schubert polynomials are polynomial representatives of Schubert classes in the cohomology of the complete flag variety and have a rich combinatorial theory. In particular, their monomial expansion is given by a bumpless pipe dream formula. Quantum double Schubert polynomials are polynomial representatives of Schubert classes in the torus-equivariant quantum cohomology of the complete flag variety, but no analogous combinatorial formulation has previously been discovered. In this talk, we will first cover the bumpless pipe dreams formula for double Schubert polynomials. Then we will introduce a generalization of the bumpless pipe dreams called quantum bumpless pipe dreams, giving a combinatorial formula for quantum double Schubert polynomials as a sum of binomial weights of quantum bumpless pipe dreams. Finally, we will give a sketch for the proof of this new formula.