The wave-particle duality of the qudit quantum space and the quantum wave gates

TL;DR

This paper introduces the concept of wave-particle duality in qudit quantum spaces, classifies elementary quantum gates via qudit functionals, and proposes a new class of quantum wave gates with physical realizations.

Contribution

It presents a novel framework linking wave-particle duality to qudit gates and introduces quantum wave gates as a new type of quantum gate.

Findings

Quantum functionals relate to states via Fourier transform and uncertainty principles.

All elementary quantum gates are classified by pairs of qudit functionals.

Quantum wave gates are a new class of gates with physical implementations.

Abstract

We propose three core ideas: 1. the wave-particle duality of the qudit quantum space; 2. the classification of all elementary quantum gates by ordered pairs of qudit functionals; 3. a new type of quantum gates called the "quantum wave gates". We first study the quantum functionals whose relation to the quantum states is analogous to that between the momentum and position wavefunctions in fundamental quantum physics: a Fourier transform and an entropic uncertainty principle can be defined between the dual representations. The quantum functionals are not just mathematical constructs but have clear physical meanings and quantum circuit realizations. Connecting the partition interpretation of the qudit functionals to the effects of quantum gates we classify all elementary quantum gates by ordered pairs of qudit functionals. By generalizing the qudit functionals to quantum functionals, the new type of "quantum wave gates" are discovered as quantum versions of the conventional quantum gates.