Deterministic sources of quantum light (i.e. single photons or pairs of entangled photons) are required for a whole host of applications in quantum technology, including quantum imaging, quantum cryptography and the long-distance transfer of quantum information in future quantum networks. Semiconductor quantum dots are ideal candidates for solid-state quantum emitters as these artificial atoms have large dipole moments and a quantum confined energy level structure, enabling the realization of single photon sources with high repetition rates and high single photon purity. Quantum dots may also be triggered using a laser pulse for on-demand operation. The naturally-occurring size variations in ensembles of quantum dots offers the potential to increase the bandwidth of quantum communication systems through wavelength-division multiplexing, but conventional laser triggering schemes based on Rabi rotations are ineffective when applied to inequivalent emitters. Here we report the demonstration of the simultaneous triggering of >10 quantum dots using adiabatic rapid passage. We show that high-fidelity quantum state inversion is possible in a system of quantum dots with a 15 meV range of optical transition energies using a single broadband, chirped laser pulse, laying the foundation for high-bandwidth, multiplexed quantum networks.