  The time-evolving matrix product operator (TEMPO) method has become a very
competitive numerical method for studying the real-time dynamics of quantum
impurity problems. For small impurities, the most challenging calculation in
TEMPO is to construct the matrix product state representation of the
Feynman-Vernon influence functional. In this work we propose an efficient
method for this task, which exploits the time-translationally invariant
property of the influence functional. The required number of matrix product
state multiplication in our method is almost independent of the total evolution
time, as compared to the method originally used in TEMPO which requires a
linearly scaling number of multiplications. The accuracy and efficiency of this
method are demonstrated for the Toulouse model and the single impurity Anderson
model.
