2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149623Linear quantum cellular automata were introduced recently as one of the models of quantum computing. A basic postulate of quantum mechanics imposes a strong constraint on any quantum machine: it has to be unitary, that is its time evolution operator has to be a unitary transformation. In this paper we give an efficient algorithm to decide if a linear quantum cellular automaton is unitary. The complexity of the algorithm is O(n^((3r-1)/(r+1))) = O(n^3) in the algebraic computational model if the automaton has a continuous neighborhood of size r, where $n$ is the size of the input.Updated for submission to SIAM Journal on Computing. Improved slightly the algorithmQuantum PhysicsComputational Complexitytext