  Physical implementation of Quantum Information Processing (QIP) by
liquid-state Nuclear Magnetic Resonance (NMR), using weakly coupled spin-1/2
nuclei of a molecule, is well established. Nuclei with spin$>$1/2 oriented in
liquid crystalline matrices is another possibility. Such systems have multiple
qubits per nuclei and large quadrupolar couplings resulting in well separated
lines in the spectrum. So far, creation of pseudopure states and logic gates
have been demonstrated in such systems using transition selective
radio-frequency pulses. In this paper we report two novel developments. First,
we implement a quantum algorithm which needs coherent superposition of states.
Second, we use evolution under quadrupolar coupling to implement multi qubit
gates. We implement Deutsch-Jozsa algorithm on a spin-3/2 (2 qubit) system. The
controlled-not operation needed to implement this algorithm has been
implemented here by evolution under the quadrupolar Hamiltonian. This method
has been implemented for the first time in quadrupolar systems. Since the
quadrupolar coupling is several orders of magnitude greater than the coupling
in weakly coupled spin-1/2 nuclei, the gate time decreases, increasing the
clock speed of the quantum computer.
