Quantum convolution and quantum correlation algorithms are physically impossible

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.

10 pages. Added reference to similar work, and fixed two typos from DCT to DFT

Cited by in corpus (2)

• The Hidden Subgroup Problem - Review and Open Problems
• Robust String Matching in O(\sqrt{N}+M) Quantum Queries