The remarkable developments in theoretical and experimental quantum computation that have been inspired by Feynman’s seminal papers on the subject are reviewed. Following an introduction to quantum computation, the implications for cryptography of quantum factoring are discussed. The requirements and challenges for practical quantum computational hardware are illustrated with an overview of the ion trap quantum computation project at Los Alamos. The physical limitations to quantum computation with trapped ions are analyzed and an assessment of the computational potential of the technology is made.

… it seems that the laws of physics present no barrier to reducing the size of computers until bits are the size of atoms, and quantum behavior holds dominant sway.” R. P. Feynman, 1985 [1].

“I think I can safely say that nobody understands quantum mechanics.” R. P. Feynman, 1965 [2].