Quantum cellular automata

A quantum cellular automaton (QCA) is an abstract model of quantum computation, devised in analogy to conventional models of cellular automata introduced by von Neumann. The same name may also refer to quantum dot cellular automata, which are a proposed physical implementation of "classical" cellular automata by exploiting quantum mechanical phenomena. QCA have attracted a lot of attention as a result of its extremely small feature size (at the molecular or even atomic scale) and its ultra-low power consumption, making it one candidate for replacing CMOS technology.

In the context of models of computation or of physical systems, quantum cellular automaton refers to the merger of elements of both (1) the study of cellular automata in conventional computer science and (2) the study of quantum information processing. In particular, the following are features of models of quantum cellular automata:

Another feature that is often considered important for a model of quantum cellular automata is that it should be universal for quantum computation (i.e. that it can efficiently simulate quantum Turing machines, some arbitrary quantum circuit or simply all other quantum cellular automata).

Models which have been proposed recently impose further conditions, e.g. that quantum cellular automata should be reversible and/or locally unitary, and have an easily determined global transition function from the rule for updating individual cells. Recent results show that these properties can be derived axiomatically, from the symmetries of the global evolution.

In 1982, Richard Feynman suggested an initial approach to quantizing a model of cellular automata. In 1985, David Deutsch presented a formal development of the subject. Later, Gerhard Grössing and Anton Zeilinger introduced the term "quantum cellular automata" to refer to a model they defined in 1988, although their model had very little in common with the concepts developed by Deutsch and so has not been developed significantly as a model of computation.

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