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Protecting information via probabilistic cellular automata.

Annie Ray^1,2,3, Raymond Laflamme^1,2,3, Aleksander Kubica^4,5

¹Institute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1, Canada.

Physical Review. E

|May 17, 2024

Summary

This summary is machine-generated.

This study explores the sweep rule, a probabilistic cellular automaton, revealing its capacity for stable information storage in classical spin models. It identifies a region of two coexisting phases and links the rule to the 2D Ising universality class.

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Area of Science:

Statistical mechanics
Complex systems
Information theory

Background:

Probabilistic cellular automata model classical spin dynamics.
These systems can function as classical memory at low temperatures, even with external magnetic fields.
Understanding information stability in noisy systems is crucial for developing robust memory solutions.

Purpose of the Study:

To analyze the behavior of the sweep rule, a specific probabilistic cellular automaton.
To map the phase diagram of the sweep rule in the temperature (T) and external magnetic field (h) plane.
To determine the universality class of the sweep rule.

Main Methods:

Analysis of probabilistic cellular automata dynamics.
Phase diagram mapping in the (T,h) plane.
Universality class identification.

Main Results:

A region with two coexisting stable phases was identified in the (T,h) plane for the sweep rule.
The sweep rule was found to belong to the weak two-dimensional Ising universality class.
Demonstrated the potential for information storage in classical spin models.

Conclusions:

The sweep rule exhibits stable phases suitable for information storage.
This research contributes to understanding local error correction in complex noisy systems.
Findings have implications for developing advanced error-correcting codes, including topological quantum codes.