Quantum computing with trapped ions, atoms and light

We first consider the basic requirements for a quantum computer, arguing fu r the attractiveness of nuclear spins as information-bearing entities, and light for the coupling which allows quantum gates. We then survey the stren gths of and immediate prospects for quantum information processing in ion t raps. We discuss decoherence and gate rates in ion traps, comparing methods based on the vibrational motion with a method based on exchange of photons in cavity QED. We then sketch the main features of a quantum computer desi gned to allow an algorithm needing 10(6) Toffoli gales on 100 logical qubit s. We find that around 200 ion traps linked by optical fibres and high-fine sse cavities could perform such an algorithm in a week to a month, using co mponents at or near current levels of technology.