  We propose a method for generating high-fidelity multipartite
spin-entanglement of ultracold atoms in an optical lattice in a short operation
time with a scalable manner, which is suitable for measurement-based quantum
computation. To perform the desired operations based on the perturbative
spin-spin interactions, we propose to actively utilize the extra degrees of
freedom (DOFs) usually neglected in the perturbative treatment but included in
the Hubbard Hamiltonian of atoms, such as, (pseudo-)charge and orbital DOFs.
Our method simultaneously achieves high fidelity, short operation time, and
scalability by overcoming the following fundamental problem: enhancing the
interaction strength for shortening operation time breaks the perturbative
condition of the interaction and inevitably induces unwanted correlations among
the spin and extra DOFs.
