Applications of Multi-Valued Quantum Algorithms

TL;DR

This paper extends key quantum algorithms to multi-valued logic using quantum Fourier transform, enabling more efficient quantum computations with fewer resources and broadening their practical applications.

Contribution

It introduces generalized multi-valued versions of Deutsch-Jozsa and Grover algorithms, improving efficiency and resource requirements over binary counterparts.

Findings

Extended Deutsch-Jozsa algorithm distinguishes constant and balanced functions in one query

Multi-valued Grover algorithm reduces qudit count and memory usage

Algorithms have practical advantages and applications in quantum computing

Abstract

This paper generalizes both the binary Deutsch-Jozsa and Grover algorithms to $n$-valued logic using the quantum Fourier transform. Our extended Deutsch-Jozsa algorithm is not only able to distinguish between constant and balanced Boolean functions in a single query, but can also find closed expressions for classes of affine logical functions in quantum oracles, accurate to a constant term. Furthermore, our multi-valued extension of the Grover algorithm for quantum database search requires fewer qudits and hence a substantially smaller memory register, as well as fewer wasted information states, to implement. We note several applications of these algorithms and their advantages over the binary cases.