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 uncertain, owing to the extremely fragile nature of quantum superpositions. A leading physical candidate for a quantum computer is a collection of trapped atomic ions. Experiments at NIST are reported in this context, including the demonstration of simple quantum logic gates and the controlled generation of entangled quantum states of up to four particles. The outlook for future quantum computing using trapped ions or alternative technologies will be discussed.

ANL Physics Division Colloquium Schedule