Provable quantum state tomography via non-convex methods

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-like 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 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.

21 pages, 26 figures, code included

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Cited by in corpus (6)

• The Non-convex Geometry of Low-rank Matrix Optimization
• Guaranteed recovery of quantum processes from few measurements
• Simple and practical algorithms for ${\ell }_p$-norm low-rank approximation
• Using non-convex optimization in quantum process tomography: Factored gradient descent is tough to beat
• Implicit regularization and solution uniqueness in over-parameterized matrix sensing
• Provably convergent acceleration in factored gradient descent with applications in matrix sensing