  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.
