Abstract

There are two major obstacles to the realization of a quantum computer : scaling and decoherence. Those are, in general, interconnected problems, since one considers as a rule of thumb that decoherence effects become more important as the size of the system increases. However, a somehow contrary reasoning may also apply : many particle Hamiltonians may display symmetries leading to the protection of collective entangled states of a generic two-level system [1]. For such systems, protection becomes more efficient with an increasing number of particles. We introduce a new kind of Hamiltonian describing an infinite range coupling between particles placed on a square array with a large number of symmetries and describe its spectral properties. We show in particular that this Hamiltonian can be naturally realized [2] using ions confined in a surface trap and that the induced protection is more effective than the one predicted for a short range Hamiltonian [1].

© 2007 IEEE