  Quantum process tomography (QPT) is a fundamental task to characterize the
dynamics of quantum systems. In contrast to standard QPT, ancilla-assisted
process tomography (AAPT) framework introduces an extra ancilla system such
that a single input state is needed. In this paper, we extend the two-stage
solution, a method originally designed for standard QPT, to perform AAPT. Our
algorithm has $O(Md_A^2d_B^2)$ computational complexity where $ M $ is the type
number of the measurement operators, $ d_A $ is the dimension of the quantum
system of interest, and $d_B$ is the dimension of the ancilla system. Then we
establish an error upper bound and further discuss the optimal design on the
input state in AAPT. A numerical example on a phase damping process
demonstrates the effectiveness of the optimal design and illustrates the
theoretical error analysis.
