In this work, we initiate the study of a new class of impulsive boundary value problems consisting of mixed type fractional quantum and Hadamard derivatives. We will establish existence and uniqueness results by using tools from the functional analysis. We prove the uniqueness result via Banach’s contraction mapping principle, while we will use the Leray-Schauder nonlinear alternative to establish an existence result. We also present examples to illustrate the obtained results.