Building a Quantum Computer Atom by Atom Christopher Monroe Department of Physics University of Michigan A quantum computer can store and process quantum superpositions of numbers. This parallelism leads to an exponential speedup over conventional computers for certain algorithms. However, the prospects for constructing a quantum computer are highly speculative, owing to the extremely fragile nature of quantum superpositions. A quantum computer is nothing more than a smaller (and more humane) version of Schroedinger's Cat, and if one is ever built, it will strongly impact both computer science and quantum mechanical foundations. Leading quantum computer hardware involves exotic systems such as individual trapped atoms, where the isolation from the environment is unparalleled. Experiments are reported in this context, where simple quantum logic gates have been demonstrated. The outlook for large-scale quantum computing with individual atoms and alternative technologies will be discussed.