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A Swin Transformer-Based Model for Thyroid Nodule Detection in Ultrasound Images

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Tensor-Network Codes.

Terry Farrelly¹, Robert J Harris¹, Nathan A McMahon^1,2

¹ARC Centre for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, St. Lucia, Queensland 4072, Australia.

Physical Review Letters

|August 6, 2021

Summary

This summary is machine-generated.

We introduce tensor-network stabilizer codes with a natural decoder. This efficient and exact decoder achieves an 18.8% threshold for holographic codes under depolarizing noise.

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Area of Science:

Quantum Information Science
Quantum Error Correction
Condensed Matter Physics

Background:

Stabilizer codes are crucial for quantum error correction.
Holographic codes offer unique properties but lack efficient decoders.
Existing decoders for holographic codes are often inefficient or inexact.

Purpose of the Study:

Introduce tensor-network stabilizer codes and their decoders.
Generalize holographic codes beyond existing constructions.
Develop an efficient and exact decoder for holographic codes.

Main Methods:

Developed a novel tensor-network stabilizer code framework.
Generalized holographic codes using tensor networks.
Implemented an exact tensor-network decoder without bond-dimension truncation.

Main Results:

Achieved an 18.8% threshold for a generalized holographic code under depolarizing noise.
Demonstrated polynomial complexity for the exact tensor-network decoder.
Showcased the decoder's efficiency against locally correlated noise.

Conclusions:

Tensor-network stabilizer codes provide a powerful framework for quantum error correction.
The developed decoder is the first efficient and exact solution for holographic codes.
This work advances the practical implementation of quantum error correction for complex code geometries.