Pure state tomography with adaptive Pauli measurements

Quantum state tomography provides a key tool for validating and fully exploiting quantum resources. However, current protocols of pure-state informationally-complete (PS-IC) measurement settings generally involve various multi-qubit gates or complex quantum algorithms, which are not practical for large systems. In this study, we present an adaptive approach to \begin{document}$N$\end{document} -qubit pure-state tomography with Pauli measurements. First, projective measurements on each qubit in the Z-direction were implemented to determine the amplitude of each base of the target state. Then, a set of Pauli measurement settings was recursively deduced by the Z-measurement results, which can be used to determine the phase of each base. The number of required measurement settings is \begin{document}$O(N)$\end{document} for certain quantum states, including cluster and W states. Finally, we numerically verified the feasibility of our strategy by reconstructing a 1-D chain state using a neural network algorithm.