  In this paper, we studied the inter-valley interactions between the orbital
functions associated with multi-valley of silicon (Si) quantum dots. Numerical
calculations show that the inter-valley coupling between orbital functions
increases rapidly with an applied electric field. We also considered the
potential applications to the quantum bit operation utilizing controlled
inter-valley interactions. Quantum bits are the multi-valley symmetric and
anti-symmetric orbitals. Evolution of these orbitals would be controlled by an
external electric field which turns on and off the inter-valley interactions.
Estimates of the decoherence time are made for the longitudinal acoustic phonon
process. Elementary single and two qubit gates are also proposed.
