Qu earned a bachelor's degree in computational mathematics from Fudan University in 1990. She came to the U.S. for graduate study, earned a master's degree in operations research at the University of Montana in 1992, and completed her Ph.D. in statistics at Pennsylvania State University in 1998. Her dissertation, jointly supervised by Bruce G. Lindsay and Bing Li, was Adaptive Generalized Estimating Equations. She joined the Oregon State University faculty in 1999, and moved to the University of Illinois in 2008. In 2015 she added another affiliation with the Institute for Genomic Biology at Illinois.