Discrete Cosine Transforms on Quantum Computers

TL;DR

This paper demonstrates that quantum computers can compute discrete cosine and sine transforms significantly faster than classical algorithms, reducing complexity from O(N log N) to O(log^2 N).

Contribution

It introduces quantum algorithms for discrete cosine and sine transforms that outperform classical methods in computational complexity.

Findings

Quantum algorithms achieve O(log^2 N) complexity for DCT and DST.

Classical algorithms require O(N log N) operations.

Quantum approach leverages superposition, entanglement, and interference.

Abstract

A classical computer does not allow to calculate a discrete cosine transform on N points in less than linear time. This trivial lower bound is no longer valid for a computer that takes advantage of quantum mechanical superposition, entanglement, and interference principles. In fact, we show that it is possible to realize the discrete cosine transforms and the discrete sine transforms of size NxN and types I,II,III, and IV with as little as O(log^2 N) operations on a quantum computer, whereas the known fast algorithms on a classical computer need O(N log N) operations.