Projected least squares: a numerically cheap quantum tomography procedure with optimal error bounds
Abstract: Quantum state tomography is the task of reconstructing the state of a quantum system from empirical data. Recent progress in the size of controllable quantum architectures has led to a new bottleneck associated with this fundamental task: scalability of classical post-processing algorithms. Projected least squares is a conceptually simple approach that addresses this issue. It is numerically cheap and and the data processing can be done online (i.e. while the experiment is running). We equip this estimation technique with rigorous, non-asymptotic error bounds. These are optimal in the sense that they saturate fundamental bounds from information theory. The method readily extends to quantum process and shadow tomography.
This is joint work with Joel Tropp (Caltech), Jonas Kahn (Toulouse), Madalin Guta (Nottingham) and Hsin Yuan Huan (Caltech).