Qubit Automaton

Jȩdrzej Stempin, Jan Wójcik, Gabriela Banaszak +4 more

We introduce a quantum analogue of a classical synchronizing automaton. In classical case the state of a system evolves according to a set of rules forming an alphabet, and sequences of these rules, called words, govern its evolution. Certain special words, known as synchronizing words, drive the automaton into a predetermined state regardless of its initial configuration. Although such an apparently irreversible process seems incompatible with the unitarity of quantum mechanics, we present a resetting protocol based on quantum synchronizing words by incorporating auxiliary qubits whose states encode the rules of the automaton's alphabet. These qubits interact with the quantum automaton, whose state is encoded in a qudit, via a global unitary operation. When the qubit register is initially prepared in a state corresponding to a synchronizing word, the automaton evolves into a predetermined pure state independent of its initial state, while the qubit register is transformed into a complex, often entangled, state that encodes information about the automaton's original configuration. The resulting entanglement depends on both the rule set and the automaton's initial state, and we show how specific entangled states can be generated within this framework.

Graham P. Collins

Giacomo Mauro D’Ariano, Chiara Macchiavello, Matteo A. C. Rossi

We introduce a quantum cellular automaton that achieves approximate phase-covariant cloning of qubits. The automaton is optimized for $1\ensuremath{\rightarrow}2N$ economical cloning. The use of the automaton for cloning allows us to exploit different foliations for improving the performance with given resources.

Charles Q. Choi

Gregory T. Huang

Norio Inui, Kazuya Nakamura, Yusuke Ide +1 more

A quantum cellular automaton, which is extended from a classical cellular automaton with Wolfram's rule 150, is studied. In contrast to the classical cellular automaton, all possible configurations exist in a quantum superposition before measurement. We show that measuring the state of only one qubit significantly aeffects the time evolution in the quantum cellular automaton. In particular, we demonstrate that, occasionally, repeating the measurement enhances the appearance of the configurations found in the classical cellular automaton. The occurrence of this enhancement is primarily determined by the results of the measurement in the early time steps, and it is sustained by a feedback mechanism.