Quantum Pseudo-fractional Fourier Transform and its application to 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.
Cite
@article{arxiv.0906.1033,
title = {Quantum Pseudo-fractional Fourier Transform and its application to quantum phase estimation},
author = {Srinivas V. Parasa and K. Eswaran},
journal= {arXiv preprint arXiv:0906.1033},
year = {2009}
}