  We present a generalized version of the discrete time quantum walk, using the
SU(2) operation as the quantum coin. By varying the coin parameters, the
quantum walk can be optimized for maximum variance subject to the functional
form $\sigma^2 \approx N^2$ and the probability distribution in the position
space can be biased. We also discuss the variation in measurement entropy with
the variation of the parameters in the SU(2) coin. Exploiting this we show how
quantum walk can be optimized for improving mixing time in an $n$-cycle and for
quantum walk search.
