  It has been proven that quantum adders are forbidden by the laws of quantum
mechanics. We analyze theoretical proposals for the implementation of
approximate quantum adders and optimize them by means of genetic algorithms,
improving previous protocols in terms of efficiency and fidelity. Furthermore,
we experimentally realize a suitable approximate quantum adder with the cloud
quantum computing facilities provided by IBM Quantum Experience. The
development of approximate quantum adders enhances the toolbox of quantum
information protocols, paving the way for novel applications in quantum
technologies.
