 Finally, each unitary transformation is not a single, sharply defined quantum logic gate, but rather a mixture
for some probability distribution formula_105 describing how well the machinery can effect the desired transformation formula_7.As a result of these effects, the actual time evolution of the state cannot be taken as an infinite-precision pure point, operated on by a sequence of arbitrarily sharp transformations, but rather as an ergodic process, or more accurately, a mixing process that only concatenates transformations onto a state, but also smears the state over time.There is no quantum analog to the push-down automaton or stack machine.