Kyrillidis, AnastasiosKalev, AmirPark, DohyungBhojanapalli, SrinadhCaramanis, ConstantineSanghavi, Sujay2018-11-092018-11-092018Kyrillidis, Anastasios, Kalev, Amir, Park, Dohyung, et al.. "Provable compressed sensing quantum state tomography via non-convex methods." <i>npj Quantum Information,</i> 4, (2018) Springer Nature: https://doi.org/10.1038/s41534-018-0080-4.https://hdl.handle.net/1911/103310With 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 setting, where only a few data points are measured from a low-rank 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 and more accurate 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 quantum state tomography problem; thus, it constitutes a provable quantum state tomography protocol.engThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.Journal articles41534-018-0080-4https://doi.org/10.1038/s41534-018-0080-4