  The density classification (DC) task, a computation which maps global density
information to local density, is studied using one-dimensional non-unitary
quantum cellular automata (QCAs). Two approaches are considered: one that
preserves the number density and one that performs majority voting. For number
preserving DC, two QCAs are introduced that reach the fixed point solution in a
time scaling quadratically with the system size. One of the QCAs is based on a
known classical probabilistic cellular automaton which has been studied in the
context of DC. The second is a new quantum model that is designed to
demonstrate additional quantum features and is restricted to only two-body
interactions. Both can be generated by continuous-time Lindblad dynamics. A
third QCA is a hybrid rule defined by both discrete-time and continuous-time
three-body interactions that is shown to solve the majority voting problem
within a time that scales linearly with the system size.
