Given an antisymmetric matrix (A) or the unitary matrix (U_A = e^A)-or an oracle whose answers can be used to infer information about (A)-in this paper we present a parameterized circuit framework that can be used to approximate a quantum circuit for (e^A). We design the circuit based on a uniform antisymmetric matrix with (\{\pm 1\}) elements, which has an eigenbasis that is a phase-shifted version of the quantum Fourier transform, and its eigenspectrum can be constructed by using rotation (Z) gates. Therefore, we show that it can be used to directly estimate (e^A) and its quantum circuit representation. Since the circuit is based on (O(n^2)) quantum gates, which form the eigendecomposition of (e^A) with separate building blocks, it can also be used to approximate the eigenvalues of (A).