  Deutsch's algorithm is the simplest quantum algorithm which shows the
acceleration of quantum computer. In this paper, we theoretically advance a
scheme to implement quantum Deutsch's algorithm in spin-orbital angular
momentum space. Our scheme exploits a newly developed optical device called
"q-plate", which can couple and manipulate the spin-orbital angular momentum
simultaneously. This experimental setup is of high stability and efficiency
theoretically for there is no interferometer in it.
