Cellular automaton decoders for topological quantum codes with noisy measurements and beyond

Area of Science:

• Quantum Information Science
• Computational Physics
• Error Correction Codes

Background:

• Quantum error correction is crucial for building fault-tolerant quantum computers.
• Topological quantum codes offer a promising avenue for error correction.
• Developing efficient and robust decoders is a key challenge.

Purpose of the Study:

• To propose a novel error correction procedure based on a cellular automaton sweep rule.
• To demonstrate its applicability beyond topological quantum codes.
• To analyze its performance and robustness, particularly against measurement errors.

Main Methods:

• The study focuses on the three-dimensional toric code on a rhombic dodecahedral lattice with boundaries.
• A cellular automaton, the sweep rule, is employed for error correction.
• Numerical benchmarking is performed using various noise models, including measurement errors.

Main Results:

• The proposed local decoder for the 3D toric code demonstrates a non-zero error threshold.
• The error correction procedure exhibits remarkable robustness against measurement errors.
• Performance is largely insensitive to specific lattice details and noise models.

Conclusions:

• The sweep rule offers a simple and high-performance decoding strategy.
• This approach is applicable to a broad range of quantum low-density parity-check codes.
• The findings represent a step towards practical quantum error correction.