Provable quantum state tomography via non-convex methods

TitleProvable quantum state tomography via non-convex methods
Publication TypeJournal Article
Year of Publication2017
AuthorsKyrillidis, A, Kalev, A, Park, D, Bhojanapalli, S, Caramanis, C, Sanghavi, S
Date Published2017/11/19

With nowadays steadily growing quantum processors, it is required to develop new quantum tomography tools that are tailored for high-dimensional systems. In this work, we describe such a computational tool, based on recent ideas from non-convex optimization. The algorithm excels in the compressed-sensing-like setting, where only a few data points are measured from a lowrank or highly-pure quantum state of a high-dimensional system. We show that the algorithm can practically be used in quantum tomography problems that are beyond the reach of convex solvers, and, moreover, is faster than other state-of-the-art non-convex approaches. Crucially, we prove that, despite being a non-convex program, under mild conditions, the algorithm is guaranteed to converge to the global minimum of the problem; thus, it constitutes a provable quantum state tomography protocol.