Quantum Inverse Fast Fourier Transform

TL;DR

This paper introduces a Quantum Inverse Fast Fourier Transform (QIFFT) algorithm that efficiently converts quantum frequency domain data back to the time domain, outperforming traditional quantum Fourier transform inversion.

Contribution

The paper develops the first QIFFT algorithm with a complete classical formulation and butterfly diagram, enhancing quantum data processing capabilities.

Findings

QIFFT outperforms regular QFT inversion in complexity

QIFFT leverages quantum parallelism for efficiency

QIFFT offers improved versatility in quantum signal processing

Abstract

In this paper, an algorithm for Quantum Inverse Fast Fourier Transform (QIFFT) is developed to work for quantum data. Analogous to a classical discrete signal, a quantum signal can be represented in Dirac notation, application of QIFFT is a tensor transformation from frequency domain to time domain. If the tensors are merely complex entries, then we get the classical scenario. We have included the complete formulation of QIFFT algorithm from the classical model and have included butterfly diagram. QIFFT outperforms regular inversion of Quantum Fourier Transform (QFT) in terms of computational complexity, quantum parallelism and improved versatility.