Encoders and Decoders for Quantum Expander Codes Using Machine Learning

TL;DR

This paper introduces machine learning-based methods to design efficient quantum encoders and decoders for expander codes, reducing memory requirements and improving performance in quantum key distribution.

Contribution

It applies reinforcement learning and neural networks to quantum coding, enabling scalable encoder and decoder design without large lookup tables.

Findings

Neural network-based quantum decoder trained with maximum a posteriori error.

Deep Q-learning optimizes generator matrices for quantum CSS codes.

Improved performance over traditional quantum expander codes.

Abstract

Quantum key distribution (QKD) allows two distant parties to share encryption keys with security based on laws of quantum mechanics. In order to share the keys, the quantum bits have to be transmitted from the sender to the receiver over a noisy quantum channel. In order to transmit this information, efficient encoders and decoders need to be designed. However, large-scale design of quantum encoders and decoders have to depend on the channel characteristics and require look-up tables which require memory that is exponential in the number of qubits. In order to alleviate that, this paper aims to design the quantum encoders and decoders for expander codes by adapting techniques from machine learning including reinforcement learning and neural networks to the quantum domain. The proposed quantum decoder trains a neural network which is trained using the maximum aposteriori error for the syndromes, eliminating the use of large lookup tables. The quantum encoder uses deep Q-learning based techniques to optimize the generator matrices in the quantum Calderbank-Shor-Steane (CSS) codes. The evaluation results demonstrate improved performance of the proposed quantum encoder and decoder designs as compared to the quantum expander codes.