  Quantum computing has been attracting tremendous efforts in recent years. One
prominent application is to perform quantum simulations of electron
correlations in large molecules and solid-state materials, where orbital
degrees of freedom are crucial to quantitatively model electronic properties.
Electron orbitals unlike quantum spins obey crystal symmetries, making the
atomic orbital in optical lattices a natural candidate to emulate electron
orbitals. Here, we construct atom-orbital qubits by manipulating $s$- and
$d$-orbitals of atomic Bose-Einstein condensation in an optical lattice.
Noise-resilient quantum gate operations are achieved by performing holonomic
quantum control, which admits geometrical protection. We find it is critical to
eliminate the orbital leakage error in the system. The gate robustness is
tested by varying the intensity of the laser forming the lattice. Our work
opens up wide opportunities for atom-orbital based quantum information
processing, of vital importance to programmable quantum simulations of
multi-orbital physics in molecules and quantum materials.
