  To advance our understanding of Quantum Cellular Automata in problem solving
through parallel and distributed computing, this research quantized the density
classification problem and adopted the Quantum Particle Automata (QPA) to solve
the quantized problem. In order to solve this problem, the QPA needed a unitary
operator to carry out the QPA evolution and a boundary partition to make the
classification decisions. We designed a Genetic Algorithm (GA) to search for
the unitary operators and the boundary partitions to classify the density of
binary inputs with length 5. The GA was able to find more than one unitary
operator that can transform the QPA in ways such that when the particle was
measured, it was more likely to collapse to the basis states that were on the
correct side of the boundary partition for the QPA to decide if the binary
input had majority density 0 or majority density 1. We analyzed these solutions
and found that the QPA evolution dynamic was driven by a particular parameter
$\theta$ of the unitary operator: a small $\theta$ gave the particle small mass
hence fast evolution while large $\theta$ had the opposite effect. While these
results are encouraging, scaling these solutions for binary inputs of arbitrary
length of $n$ requires additional analysis, which we will investigate in our
future work.
