Our ability to control and exploit quantum phenomena - the often counterintuitive behavior of energy and matter at the atomic scale - is still at a very primitive stage, analogous to the demonstration of the first transistor. A challenging goal is to learn how to scale up from simple systems of a few components to the sizes and complexity necessary for applications.

As an example, it has been shown that a quantum computer can in principle rapidly factor large numbers, a mathematical problem whose difficulty provides the security of our currently used "public key" encryption algorithms.

Constructing such a device, however, will require numerous advances in the areas of coherent quantum phenomena as we learn how to preserve the "quantumness" of systems while still exerting control over them. Unfortunately, the properties that make a quantum computer powerful are difficult to maintain in large systems. We have much to learn about individual quantum systems, how to connect them, how to control them, how to measure them, and how to fix the inevitable errors.

Some of the topics being studied are:

• * Quantum properties of superconducting qubits
• * Quantum entanglement, control, and transport of atoms in cavities and optical lattices
• * Decoherence studies with atoms and condensed matter systems.
• * Spin- and charge-based quantum computing
• * Topological quantum computing
• * Quantum coherence and entanglement
• * The quantum-classical interface
• * Quasi-one-dimensional superconductors as optical lattices
• * Quantum computing with the fractional quantum Hall effect