TL;DR
This paper identifies elementary cellular automata rules that can be simulated with quantum circuits and provides efficient quantum circuit implementations for each, advancing the understanding of quantum simulation of classical automata.
Contribution
It presents a complete list of 22 elementary cellular automata rules simulatable by quantum circuits and offers $O(N)$ gate implementations for each rule.
Findings
22 automata rules can be simulated quantum mechanically
Quantum circuits for these rules require $O(N)$ gates
Provides explicit quantum circuit constructions for each rule
Abstract
In this paper we identify full list of Elementary Cellular Automata rules which can be simulated using a quantum circuit (there are 22 such rules). For every such rule we present quantum circuit implementing it with gates.
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