  The experimental implementation of selective quantum process tomography
(SQPT) involves computing individual elements of the process matrix with the
help of a special set of states called quantum 2-design states. However, the
number of experimental settings required to prepare input states from quantum
2-design states to selectively and precisely compute a desired element of the
process matrix is still high, and hence constructing the corresponding unitary
operations in the lab is a daunting task. In order to reduce the experimental
complexity, we mathematically reformulated the standard SQPT problem, which we
term the modified SQPT (MSQPT) method. We designed the generalized quantum
circuit to prepare the required set of input states and formulated an efficient
measurement strategy aimed at minimizing the experimental cost of SQPT. We
experimentally demonstrated the MSQPT protocol on the IBM QX2 cloud quantum
processor and selectively characterized various two- and three-qubit quantum
gates.
