In this paper we present a quantization of Cellular Automata. Our formalism
is based on a lattice of qudits, and an update rule consisting of local unitary
operators that commute with their own lattice translations. One purpose of this
model is to act as a theoretical model of quantum computation, similar to the
quantum circuit model. It is also shown to be an appropriate abstraction for
space-homogeneous quantum phenomena, such as quantum lattice gases, spin chains
and others. Some results that show the benefits of basing the model on local
unitary operators are shown: universality, strong connections to the circuit
model, simple implementation on quantum hardware, and a wealth of applications.
%0 Generic
%1 perezdelgado2007local
%A Perez-Delgado, Carlos A.
%A Cheung, Donny
%D 2007
%K automata cellular combinatorial unitary
%R 10.1103/PhysRevA.76.032320
%T Local Unitary Quantum Cellular Automata
%U http://arxiv.org/abs/0709.0006
%X In this paper we present a quantization of Cellular Automata. Our formalism
is based on a lattice of qudits, and an update rule consisting of local unitary
operators that commute with their own lattice translations. One purpose of this
model is to act as a theoretical model of quantum computation, similar to the
quantum circuit model. It is also shown to be an appropriate abstraction for
space-homogeneous quantum phenomena, such as quantum lattice gases, spin chains
and others. Some results that show the benefits of basing the model on local
unitary operators are shown: universality, strong connections to the circuit
model, simple implementation on quantum hardware, and a wealth of applications.
@misc{perezdelgado2007local,
abstract = {In this paper we present a quantization of Cellular Automata. Our formalism
is based on a lattice of qudits, and an update rule consisting of local unitary
operators that commute with their own lattice translations. One purpose of this
model is to act as a theoretical model of quantum computation, similar to the
quantum circuit model. It is also shown to be an appropriate abstraction for
space-homogeneous quantum phenomena, such as quantum lattice gases, spin chains
and others. Some results that show the benefits of basing the model on local
unitary operators are shown: universality, strong connections to the circuit
model, simple implementation on quantum hardware, and a wealth of applications.},
added-at = {2013-12-23T05:06:18.000+0100},
author = {Perez-Delgado, Carlos A. and Cheung, Donny},
biburl = {https://www.bibsonomy.org/bibtex/269c8e9cb5a0262790204e949e044aaa3/aeu_research},
description = {Local Unitary Quantum Cellular Automata},
doi = {10.1103/PhysRevA.76.032320},
interhash = {032f5b1ef288fe1b878fa32b0272cef1},
intrahash = {69c8e9cb5a0262790204e949e044aaa3},
keywords = {automata cellular combinatorial unitary},
note = {cite arxiv:0709.0006Comment: To appear in Physical Review A},
timestamp = {2013-12-23T08:22:34.000+0100},
title = {Local Unitary Quantum Cellular Automata},
url = {http://arxiv.org/abs/0709.0006},
year = 2007
}