Quantum Pseudo-fractional Fourier Transform and its application to quantum phase estimation

TL;DR

This paper introduces a quantum algorithm for computing fractional Fourier transform coefficients efficiently using polynomial complexity gates, and demonstrates its application to quantum phase estimation.

Contribution

It develops a unitary quantum pseudo-fractional Fourier transform operator, enabling efficient computation of FrFT coefficients and applying it to quantum phase estimation.

Findings

Polynomial complexity (O(n^3)) for quantum FrFT computation.

Introduction of a unitary operator U for implementing QPFrFT.

Application of QPFrFT to enhance quantum phase estimation.

Abstract

- In this paper we present a method to compute the coefficients of the fractional Fourier transform (FrFT) on a quantum computer using quantum gates of polynomial complexity of the order O(n^3). The FrFt, a generalization of the DFT, has wide applications in signal processing and is particularly useful to implement the Pseudopolar and Radon transforms. Even though the FrFT is a non-unitary operation, to develop its quantum counterpart, we develop a unitary operator called the quantum Pseudo-fraction Fourier Transform (QPFrFT) in a higher-dimensional Hilbert space, in order to computer the coefficients of the FrFT. In this process we develop a unitary operator denoted U by which is an essential step to implement the QPFrFT. We then show the application of the operator U in the problem of quantum phase estimation.