Scalable register initialization for quantum computing in an optical lattice

The Mott insulator state created by loading an atomic Bose-Einstein
condensate (BEC) into an optical lattice may be used as a means to prepare a
register of atomic qubits in a quantum computer. Such architecture requires a
lattice commensurately filled with atoms, which corresponds to the insulator
state only in the limit of zero inter-well tunneling. We show that a lattice
with spatial inhomogeneity created by a quadratic magnetic trapping potential
can be used to isolate a subspace in the center which is impervious to
hole-hoping. Components of the wavefunction with more than one atom in any well
can be projected out by selective measurement on a molecular photo-associative
transition. Maintaining the molecular coupling induces a quantum Zeno effect
that can sustain a commensurately filled register for the duration of a quantum
computation.