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Nonequilibrium Phase Transitions in (1+1)-Dimensional Quantum Cellular Automata with Controllable Quantum
Edward Gillman1,2, Federico Carollo3, Igor Lesanovsky1,2,3
1School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom.
We introduce quantum generalizations of cellular automata that exhibit stationary behavior and phase transitions in isolated systems. Quantum correlations impact dynamics and phase transitions, efficiently represented by tensor networks.
Area of Science:
- Quantum physics
- Many-body systems
- Statistical mechanics
Background:
- Recent advances in Rydberg atom quantum simulators motivate new theoretical models.
- Nonequilibrium many-body systems in isolation present unique challenges for understanding dynamics and phase transitions.
Purpose of the Study:
- To introduce and investigate the dynamics of (1+1)-dimensional quantum cellular automata.
- To explore the role of quantum correlations in nonequilibrium phase transitions.
- To assess the efficiency of tensor network methods for representing these quantum systems.
Main Methods:
- Development of quantum generalizations of the Domany-Kinzel cellular automaton.
- Analysis of stationary behavior and nonequilibrium phase transitions in isolated systems.
- Utilizing projected entangled pair state tensor networks for system representation and analysis.
Main Results:
- Demonstrated stationary behavior and nonequilibrium phase transitions in isolated quantum cellular automata.
- Showcased the ability to controllably introduce local quantum correlations.
- Established tensor networks as an efficient method for representing these automata, with complexity reflecting quantumness.
Conclusions:
- Quantum cellular automata can exhibit complex dynamics and phase transitions even in isolation.
- Quantum correlations significantly influence the behavior of these systems.
- Tensor network methods provide a powerful tool for studying quantum many-body dynamics and complexity.
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