Efficient quantum state estimation with low-rank matrix completion

This paper introduces a novel and efficient technique for quantum state estimation,
coined as low-rank matrix-completion quantum state tomography for characterizing
pure quantum states, as it requires only non-entangling bases and 2n + 1 local Pauli
operators. This significantly reduces the complexity of the process and increases the
accuracy of the state estimation, as it eliminates the need for the entangling bases,
which are experimentally difficult to implement on quantum devices. The required
minimal post-processing, improved accuracy and efficacy of this
matrix-completion-based method make it an ideal benchmarking tool for
investigating the properties of quantum systems, enabling researchers to verify the
accuracy of quantum devices, characterize their performance, and explore the
underlying physics of quantum phenomena. Our numerical results demonstrate that
this method outperforms contemporary techniques in its ability to accurately
reconstruct multi-qubit quantum states on real quantum devices, making it an
invaluable contribution to the field of quantum state characterization and an
essential step toward the reliable deployment of intermediate- and large-scale
quantum devices.