Abstract
Quantum computers require the storage of quantum information in a set of two-level systems (called qubits), the processing of this information using quantum gates and a means of final readout1. So far, only a few systems have been identified as potentially viable quantum computer models—accurate quantum control of the coherent evolution is required in order to realize gate operations, while at the same time decoherence must be avoided. Examples include quantum optical systems (such as those utilizing trapped ions2,3,4,5,6,7,8,9 or neutral atoms10,11,12, cavity quantum electrodynamics13,14,15 and nuclear magnetic resonance16,17) and solid state systems (using nuclear spins1,18, quantum dots19 and Josephson junctions20). The most advanced candidates are the quantum optical and nuclear magnetic resonance systems, and we expect that they will allow quantum computing with about ten qubits within the next few years. This is still far from the numbers required for useful applications: for example, the factorization of a 200-digit number requires about 3,500 qubits21, rising to 100,000 if error correction22 is implemented. Scalability of proposed quantum computer architectures to many qubits is thus of central importance. Here we propose a model for an ion trap quantum computer that combines scalability (a feature usually associated with solid state proposals) with the advantages of quantum optical systems (in particular, quantum control and long decoherence times).

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