  Here, a new two-dimensional process, discrete in time and space, that yields
the results of both a random walk and a quantum random walk, is introduced.
This model describes the population distribution of four coin states |1>,-|1>,
|0> -|0> in space without interference, instead of two coin states |1>, |0>
.For the case of no boundary conditions, the model is similar to a Markov chain
with a stochastic matrix, i.e., it conserves the population distribution of the
four coin states, and by using a proper transformation, yield probability
distributions of the two quantum states |1>, |0> in space, similar to a unitary
operator. Numerical results for a quantum random walk on infinite and finite
lines are introduced.
