  Constraint satisfiability problems, crucial to several applications, are
solved on a quantum computer using Grover's search algorithm, leading to a
quadratic improvement over the classical case. The solutions are obtained with
high probability for several cases and are illustrated for the cases involving
two variables for both 3- and 4-bit numbers. Methods are defined for inequality
comparisons, and these are combined according to the form of the satisfiability
formula, to form the oracle for the algorithm. The circuit is constructed using
IBM Qiskit and is verified on an IBM simulator. It is further executed on one
of the Noisy Intermediate-Scale Quantum (NISQ) processors from IBM on the
cloud. Noise levels in the processor at present are found to be too high for
successful execution. Running the algorithm on the simulator with a custom
noise model lets us identify the noise threshold for successful execution.
