From Dirac to Diffusion: Decoherence in Quantum Lattice Gases
Quantum Information Processing
One-Dimensional Quantum Cellular Automata over Finite, Unbounded Configurations
Language and Automata Theory and Applications
Intrinsically Universal One-dimensional Quantum Cellular Automata in Two Flavours
Fundamenta Informaticae - Machines, Computations and Universality, Part II
Algebraic characterizations of unitary linear quantum cellular automata
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Intrinsically Universal One-dimensional Quantum Cellular Automata in Two Flavours
Fundamenta Informaticae - Machines, Computations and Universality, Part II
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Linear 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(n3) in the algebraic computational model if the automaton has a continuous neighborhood of size r, where n is the size of the input.