# Quantum‐Inspired Fourier Transforms Based on Circuits

## TL;DR

This paper introduces a classical circuit-based Fourier transform inspired by quantum computing, achieving faster processing speeds than traditional methods.

## Contribution

A novel classical circuit scheme that emulates quantum Fourier transform with correlated electrical signals and faster computation.

## Key findings

- The circuit-based Fourier transform matches the speed of quantum FT algorithms.
- Classical circuits can emulate quantum gates and perform efficient signal processing.
- Experimental verification was conducted for processors with 2, 3, and 5 qubits.

## Abstract

Fourier transform (FT) is ubiquitous in modern society due to their broad applications in many branches of science and engineering. Improving the speed of FT is a common interest in the fields of signal processing. The quantum FT is generally believed to be superior to classical algorithms, but it requires a special quantum environment to perform, which has not yet been widely used. Inspired by quantum FT, here a new FT scheme is demonstrated based on circuits. In the circuit scheme, a new type of classical correlation, which its mathematical form corresponds to those of quantum entanglement, has been constructed. The calculation speed using the designed circuit scheme is equivalent to those based on the quantum FT algorithms, which is faster than those based on the classical fast FT algorithms. Furthermore, some basic gates have been designed and experimentally fabricated using classical circuit networks, which can emulate the functions of quantum gates. Fast calculation efficiencies for the FT based on the designed classical circuit networks have been demonstrated. Extensive applications of the FT scheme in the signal processing are anticipated.

An analog scheme of classical circuit for the quantum Fourier transform is proposed. The number of the basic computing components employed in the circuit design is consistent with the number of the quantum gate in the quantum circuit. The information is encoded using correlated electrical signals. This makes the classical circuit network have processing functions similar to that of quantum computation. Furthermore, an experimental verification on the analogy of the two, three and five qubit processors is presented.