On Quantum Cellular Automata
<|reference_start|>On Quantum Cellular Automata: In recent work [quant-ph/0405174] by Schumacher and Werner was discussed an abstract algebraic approach to a model of reversible quantum cellular automata (CA) on a lattice. It was used special model of CA based on partitioning scheme and so there is a question about quantum CA derived from more general, standard model of classical CA. In present work is considered an approach to definition of a scheme with "history", valid for quantization both irreversible and reversible classical CA directly using local transition rules. It is used language of vectors in Hilbert spaces instead of C*-algebras, but results may be compared in some cases. Finally, the quantum lattice gases, quantum walk and "bots" are also discussed briefly.<|reference_end|>
@article{vlasov2004on,
    title={On Quantum Cellular Automata},
    author={Alexander Yu. Vlasov},
    journal={arXiv preprint arXiv:quant-ph/0406119},
    year={2004},
    archivePrefix={arXiv},
    eprint={quant-ph/0406119},
    primaryClass={quant-ph cs.OH nlin.CG}
}