Protecting information via probabilistic cellular automata

Abstract

Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature $T$, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic field $h$. In this article, we study a recently-introduced probabilistic cellular automaton, the sweep rule, and map out a region of two coexisting stable phases in the $(T,h)$ plane. We also find that the sweep rule belongs to the weak two-dimensional Ising universality class. Our work is a step towards understanding how simple geometrically-local error-correction strategies can protect information encoded into complex noisy systems, such as topological quantum error-correcting codes.

arXiv comment7+6.5 pages, 19 figures

References in corpus (14)

• Fault-tolerant quantum computation by anyons
• Topological quantum memory
• Quantum Error Correction for Quantum Memories
• Topological Quantum Distillation
• Quantum memories at finite temperature
• Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
• Quantum memories based on engineered dissipation
• Universal topological phase of 2D stabilizer codes
• Statistical mechanical models for quantum codes with correlated noise
• Cellular-automaton decoders with provable thresholds for topological codes
• Three-dimensional color code thresholds via statistical-mechanical mapping
• Cellular automaton decoders for topological quantum codes with noisy measurements and beyond
• Clifford-deformed Surface Codes
• Efficient color code decoders in $d\ge 2$ dimensions from toric code decoders

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