# Provable quantum state tomography via non-convex methods

arXiv: https://arxiv.org/abs/1711.02524 · HTML: https://mlsanity.com/paper/1711.02524/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2017.

## Built on by (most cited first, 2 of 2)

- [Fast quantum state reconstruction via accelerated non-convex programming](https://mlsanity.com/paper/2104.07006/) (2021)
- [One Rank at a Time: Cascading Error Dynamics in Sequential Learning](https://mlsanity.com/paper/2505.22602/) (2025)

## Abstract (arXiv)

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.