A Comprehensive Study of Quantum Arithmetic Circuits

TL;DR

This paper provides a comprehensive review of quantum arithmetic circuits, detailing their designs, implementations, efficiencies, and applications, serving as a valuable resource for advancing quantum algorithm development.

Contribution

It offers a systematic overview of current quantum arithmetic circuit designs, including detailed implementations and efficiency evaluations, highlighting future research directions.

Findings

Detailed quantum implementations of arithmetic operations

Evaluation of circuit efficiencies for various objectives

Discussion of applications and future research avenues

Abstract

In recent decades, the field of quantum computing has experienced remarkable progress. This progress is marked by the superior performance of many quantum algorithms compared to their classical counterparts, with Shor's algorithm serving as a prominent illustration. Quantum arithmetic circuits, which are the fundamental building blocks in numerous quantum algorithms, have attracted much attention. Despite extensive exploration of various designs in the existing literature, researchers remain keen on developing novel designs and improving existing ones. In this review article, we aim to provide a systematically organized and easily comprehensible overview of the current state-of-the-art in quantum arithmetic circuits. Specifically, this study covers fundamental operations such as addition, subtraction, multiplication, division and modular exponentiation. We delve into the detailed quantum implementations of these prominent designs and evaluate their efficiency considering various objectives. We also discuss potential applications of presented arithmetic circuits and suggest future research directions.