Our paper on fast and provable non-convex algorithms for quantum state tomography is accepted at Nature’s Journal on Quantum Information.

Abstract. 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 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.

See also the Editorial summary:

Summary. Quantum tomography: efficient identification of quantum states from few data points A new algorithm carries out quantum tomography of large quantum states more quickly and accurately than existing alternatives. The reconstruction of quantum states from experimental data, quantum tomography, is an extremely demanding process. Even with the application of compressed sensing, which reduces the amount of experimental data required, tomography remains in practice computationally challenging. Known algorithms for quantum tomography rely on convex programs, which guarantee convergence to an output, but have a high computational complexity. Anastasios Kyrillidis from the IBM T. J. Watson Research Centre and co-workers from the USA have now developed a non-convex algorithm for quantum tomography of almost-pure quantum states that performs much better than convex analogues, as demonstrated on a 13-qubits problem. At the same time, the authors could rigorously guarantee the algorithm’s convergence in practically relevant cases.

The online version of the paper can be found here.