  There are quantum algorithms for finding a function $f$ satisfying a set of
conditions, such as solving partial differential equations, and these achieve
exponential quantum speedup compared to existing classical methods, especially
when the number $d$ of the variables of $f$ is large. In general, however,
these algorithms output the quantum state which encodes $f$ in the amplitudes,
and reading out the values of $f$ as classical data from such a state can be so
time-consuming that the quantum speedup is ruined. In this study, we propose a
general method for this function readout task. Based on the function
approximation by a combination of tensor network and orthogonal function
expansion, we present a quantum circuit and its optimization procedure to
obtain an approximating function of $f$ that has a polynomial number of degrees
of freedom with respect to $d$ and is efficiently evaluable on a classical
computer. We also conducted a numerical experiment to approximate a
finance-motivated function to demonstrate that our method works.
