  Quantum Phase Estimation (QPE) stands as a pivotal quantum computing
subroutine that necessitates an inverse Quantum Fourier Transform (QFT).
However, it is imperative to recognize that enhancing the precision of the
estimation inevitably results in a significantly deeper circuit. We developed a
variational quantum circuit (VQC) approximation to reduce the depth of the QPE
circuit, yielding enhanced performance in noisy simulations and real hardware.
Our experiments demonstrated that the VQC outperformed both Noisy QPE and
standard QPE on real hardware by reducing circuit noise. This VQC integration
into quantum compilers as an intermediate step between input and transpiled
circuits holds significant promise for quantum algorithms with deep circuits.
Future research will explore its potential applicability across various quantum
computing hardware architectures.
