A survey on the complexity of learning quantum states
This is an incremental survey that synthesizes existing research to guide future work in quantum state learning.
The paper surveys recent results on the complexity of learning quantum states, including quantum tomography and alternative models, and distills 25 open questions to advance the field.
We survey various recent results that rigorously study the complexity of learning quantum states. These include progress on quantum tomography, learning physical quantum states, alternate learning models to tomography and learning classical functions encoded as quantum states. We highlight how these results are paving the way for a highly successful theory with a range of exciting open questions. To this end, we distill 25 open questions from these results.