The successful transition from core-collapse supernova simulations using classical neutrino transport to simulations using quantum neutrino transport will require the development of methods for calculating neutrino flavor transformations that mitigate the computational expense. One potential approach is the use of angular moments of the neutrino field, which has the added appeal that there already exist simulation codes which make use of moments for classical neutrino transport. Evolution equations for quantum moments based on the quantum kinetic equations can be straightforwardly generalized from the evolution of classical moments based on the Boltzmann equation. We present an efficient implementation of neutrino transformation using quantum angular moments in the free streaming, spherically symmetric bulb model. We compare the results against analytic solutions and the results from more exact multi-angle neutrino flavor evolution calculations. We find that our moment-based methods employing scalar closures predict, with good accuracy, the onset of collective flavor transformations seen in the multi-angle results. However in some situations they overestimate the coherence of neutrinos traveling along different trajectories. More sophisticated quantum closures may improve the agreement between the inexpensive moment-based methods and the multi-angle approach.