  Robust, accurate and efficient quantum tomography is key for future quantum
technologies. Traditional methods are impractical for even medium sized systems
and are not robust against noise and errors. Here we report on an experimental
demonstration of self-guided quantum tomography; an autonomous, fast, robust
and precise technique for measuring quantum states with significantly less
computational resources than standard techniques. The quantum state is
iteratively learned by treating tomography as a projection measurement
optimization problem. We experimentally demonstrate robustness against both
statistical noise and experimental errors on both single qubit and entangled
two-qubit states. Our demonstration provides a method of full quantum state
characterization in current and near-future experiments where standard
techniques are unfeasible.
