Quantum circuit for the fast Fourier transform

TL;DR

This paper presents a quantum circuit implementation of the fast Fourier transform (FFT) that differs from the quantum Fourier transform, emphasizing data storage efficiency and versatility for quantum image processing.

Contribution

The paper introduces a novel quantum circuit for FFT that avoids garbage bits and enhances data storage efficiency, distinct from traditional QFT approaches.

Findings

Efficient quantum circuit for FFT without garbage bits

Enhanced data storage capabilities for quantum image processing

Versatile implementation suitable for various quantum algorithms

Abstract

We propose an implementation of the algorithm for the fast Fourier transform (FFT) as a quantum circuit consisting of a combination of some quantum gates. In our implementation, a data sequence is expressed by a tensor product of vector spaces. Namely, our FFT is defined as a transformation of the tensor product of quantum states. It is essentially different from the so-called quantum Fourier transform (QFT) defined to be a linear transformation of the amplitudes for the superposition of quantum states. The quantum circuit for the FFT consists of several circuits for elementary arithmetic operations such as a quantum adder, subtractor and shift operations, which are implemented as effectively as possible. Namely, our circuit does not generate any garbage bits. The advantages of our method compared to the QFT are its high versatility, and data storage efficiency in terms, for instance, of the quantum image processing.