Machine learning has recently inspired the development of a neural-network representation of quantum states capable of approximating complex (pure) states of large quantum systems. We discuss its application in performing tomography of pure quantum states as well as a scheme that promotes it to mixed state tomography. This promotion is done via a step-wise reconstruction of the eigen-states of the mixed state and works for any pure state tomography procedure. We compare this iterative method to compressed-sensing inspired methods that aim to reconstruct rank-r approximations in a single-shot manner.

Research: https://arxiv.org/search/quant-ph?searchtype=author&query=Melkani%2C%20A