Quantum convolution and quantum correlation algorithms are physically impossible

TL;DR

This paper proves that fundamental quantum algorithms for convolution and correlation, based on classical Fourier transform techniques, are physically impossible to implement within the laws of quantum mechanics.

Contribution

It demonstrates that the core step of classical convolution and correlation algorithms cannot be physically realized on quantum states, establishing fundamental limits.

Findings

Componentwise multiplication after Fourier transforms is physically impossible on quantum states.

Quantum convolution and correlation of quantum coefficients violate quantum mechanics.

The paper sets fundamental limits on quantum algorithms for these operations.

Abstract

The key step in classical convolution and correlation algorithms, the componentwise multiplication of vectors after initial Fourier Transforms, is shown to be physically impossible to do on quantum states. Then this is used to show that computing the convolution or correlation of quantum state coefficients violates quantum mechanics, making convolution and correlation of quantum coefficients physically impossible.