  Quantum device characterization via state tomography plays an important role
in both validating quantum hardware and processing quantum information, but it
needs the exponential number of the measurements. For the systems with
XX+YY-type couplings and Z readouts, such as superconducting quantum computing
(SQC) systems, traditional quantum state tomography (QST) using single-qubit
readout operations at least requires $3^n$ measurement settings in
reconstructing an $n$-qubit state. In this work, I proposed an improved QST by
adding 2-qubit evolutions as the readout operations and obtained an optimal
tomographic scheme using the integer programming optimization. I respectively
apply the new scheme on SQC systems with the Nearest-Neighbor, 2-Dimensional,
and All-to-All connectivities on qubits. It shows that this method can reduce
the number of measurements by over 60% compared with the traditional QST.
Besides, comparison with the traditional scheme in the experimental feasibility
and robustness against errors were made by numerical simulation. It is found
that, the new scheme has good implementability and it can achieve comparable or
even better accuracy than the traditional scheme. It is expected that the
experimentalist from the related fields can directly utilize the ready-made
results for reconstructing quantum states involved in their research.
