  The deployment of intermediate- and large-scale quantum devices necessitates
the development of efficient full state tomographical techniques for quantum
benchmarks. Here, we introduce a matrix filling-based method for tomography of
pure quantum states, called the matrix-completion quantum state tomography.
This method requires only 2n + 1 local Pauli operators and minimal
post-processing for n-qubit states. Numerical results show that our method is
highly efficient on superconducting real quantum devices and achieves better
fidelity estimates of multiqubit quantum states as compared to contemporary
pure state tomography methods. These desirable features of the
matrix-completion quantum state tomography protocol make it suitable for the
benchmarking of intermediate- and large-scale quantum devices dealing mainly
with pure quantum states.
