On the Irresistible Efficiency of Signal Processing Methods in Quantum Computing

TL;DR

This paper demonstrates that several classical signal transforms can be efficiently implemented on quantum computers using a logarithmic number of gates, significantly advancing quantum signal processing capabilities.

Contribution

It introduces quantum circuits for various classical signal transforms and proves their implementation requires at most O(log^2 N) gates, highlighting their efficiency.

Findings

Quantum circuits for DCT, DST, and Hartley transforms are derived.

All transforms can be implemented with at most O(log^2 N) gates.

Efficient quantum realization of classical signal transforms is feasible.

Abstract

We show that many well-known signal transforms allow highly efficient realizations on a quantum computer. We explain some elementary quantum circuits and review the construction of the Quantum Fourier Transform. We derive quantum circuits for the Discrete Cosine and Sine Transforms, and for the Discrete Hartley transform. We show that at most O(log^2 N) elementary quantum gates are necessary to implement any of those transforms for input sequences of length N.