Matrix-Completion Quantum State Tomography

Abstract: 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.