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Cellular-Automaton Decoders with Provable Thresholds for Topological Codes.

Aleksander Kubica1,2, John Preskill3,4

  • 1Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.

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We introduce a new sweep rule for cellular automata (CA) to create a sweep decoder for quantum error correction. This new method offers provable error-correction thresholds for topological quantum codes.

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Area of Science:

  • Quantum Information Science
  • Computational Physics
  • Materials Science

Background:

  • Topological quantum codes are crucial for fault-tolerant quantum computing.
  • Existing decoders often lack rigorous performance bounds or generalizability.
  • Cellular automata offer a framework for designing efficient local decoding algorithms.

Purpose of the Study:

  • To introduce a novel cellular automaton, the sweep rule, generalizing Toom's rule.
  • To develop a sweep decoder for the d≥3 dimensional toric code with provable performance.
  • To explore new cellular automaton decoders for other topological quantum codes.

Main Methods:

  • Generalization of Toom's rule to create the sweep rule for cellular automata.
  • Design and analysis of the sweep decoder for the d≥3 dimensional toric code.
  • Numerical estimation of the sweep decoder threshold for the 3D toric code under phase-flip noise.

Main Results:

  • Rigorous establishment of a lower bound on the sweep decoder's performance.
  • Numerical estimation of the sweep decoder threshold for the 3D toric code on cubic and BCC lattices.
  • Demonstration of the sweep rule's applicability to other topological codes like the color code.

Conclusions:

  • The sweep rule provides a powerful new tool for designing local decoders for topological quantum codes.
  • The sweep decoder offers provable error-correction capabilities, advancing fault-tolerant quantum computing.
  • This work opens avenues for developing new cellular automaton-based decoders for various quantum error correction schemes.