  Quantum circuits generating probability distributions has applications in
several areas. Areas like finance require quantum circuits that can generate
distributions that mimic some given data pattern. Hamiltonian simulations
require circuits that can initialize the wave function of a physical quantum
system. These wave functions, in several cases, are identical to some very well
known probability distributions. In this paper we discuss ways to construct
parameterized quantum circuits that can generate both symmetric as well as
asymmetric distributions. We follow the trajectory of quantum states as single
and two qubit operations get applied to the system, and find out the best
possible way to arrive at the desired distribution. The parameters are
optimized by a variational solver. We present results from both simulators as
well as real IBM quantum hardwares.

Quantum Physics