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 adapt-ive approach to N-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 measure-ment 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 O(N)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.