Several proposals for quantum computation utilize a lattice-type architecture with qubits trapped by a periodic potential. For systems undergoing many-body interactions described by the Bose-Hubbard Hamiltonian, the ground state carries number fluctuations that scale with the number of qubits. This process degrades the initialization of the quantum computer register. In an earlier manuscript we proposed a solution to this problem tailored to the loading of cold atoms into an optical lattice via the Mott insulator phase transition. It was shown that, by introducing an inhomogeneity to the lattice and performing a continuous measurement, the unit filled state suitable for a quantum computer register can be maintained. Here, we give a more rigorous derivation of the register fidelity in homogeneous and inhomogeneous lattices and provide evidence that the protocol is effective in the finite temperature regime.