  This article proposes quantum processing in an optical lattice, using Rydberg
electron's Fermi scattering from ground-state atoms in spin-dependent lattices
as a source of interaction. Instead of relying on Rydberg pair potentials, the
interaction is controlled by engineering the electron cloud of a sole Rydberg
atom. Here we specifically propose the implementation of two prominent
multi-qubit gates i.e. the stabilizer-phase operator and the Toffoli gate. The
new scheme addresses the main bottleneck in Rydberg quantum simulation by
suppressing the population of short-lived Rydberg states over multi-qubit
operations. This scheme mitigates different competing infidelity criteria,
eliminates unwanted cross-talks, and allows operations in dense atomic
lattices. The restoring forces in the molecule type Ryd-Fermi potential
preserve the trapping over a long interaction period. The features in the new
scheme are of special interest for the implementation of quantum optimization
and error correction algorithms.
