  It was recently proposed to use small groups of trapped ions as qubit
carriers in miniaturized electrode arrays that comprise a large number of
individual trapping zones, between which ions could be moved. This approach
might be scalable for quantum information processing with a large numbers of
qubits. Processing of quantum information is achieved by transporting ions to
and from separate memory and qubit manipulation zones in between quantum logic
operations. The transport of ion groups in this scheme plays a major role and
requires precise experimental control and fast transport. In this paper we
introduce a theoretical framework to study ion transport in external potentials
that might be created by typical miniaturized Paul trap electrode arrays. In
particular we discuss the relationship between classical and quantum
descriptions of the transport and study the energy transfer to the oscillatory
motion during near-adiabatic transport. Based on our findings we suggest a
numerical method to find electrode potentials as a function of time to optimize
the local potential an ion experiences during transport. We demonstrate this
method for one specific electrode geometry that should closely represent the
situation encountered in realistic trap arrays.
