A review on reversible quantum adders

Reversible adders are essential circuits in quantum computing systems. They are a fundamental part of the algorithms implemented for such systems, where Shor's celebrated factoring algorithm is one of the most prominent examples in which reversible arithmetic is needed. There is a wide variety of works in the existing literature which tackle the design of an adder for quantum systems, and today there is still a great interest in the creation of new designs and the perfection of the existing ones. Similar to how it happens in classical digital systems, there are different methodologies to approach the addition using reversible circuits. Some methodologies focus on minimizing the necessary resources, others on optimizing computing time, etc. In this work we analyze the reversible adders in the state-of-the-art for quantum computing, classifying them according to their type, and finally, comparing each other using referenced and validated metrics that allow highlighting the strengths and weaknesses of each adder.