Efficiently decoding quantum errors with machine learning

Debasmita Bhoumik, Ritajit Majumdar, Dhiraj Madan +3 more

Error syndromes for heavy hexagonal code and other topological codes such as surface code have typically been decoded by using Minimum Weight Perfect Matching– (MWPM) based methods. Recent advances have shown that topological codes can be efficiently decoded by deploying machine learning (ML) techniques, in particular with neural networks. In this work, we first propose an ML-based decoder for heavy hexagonal code and establish its efficiency in terms of the values of threshold and pseudo-threshold for various noise models. We show that the proposed ML-based decoding method achieves ~ 5 × higher values of threshold than that for MWPM. Next, exploiting the property of subsystem codes, we define gauge equivalence for heavy hexagonal code, by which two distinct errors can belong to the same error class. A linear search-based method is proposed for determining the equivalent error classes. This provides a quadratic reduction in the number of error classes to be considered for both bit flip and phase flip errors and thus a further improvement of ~ 14% in the threshold over the basic ML decoder. Last, a novel technique based on rank to determine the equivalent error classes is presented, which is empirically faster than the one based on linear search.

Haoran Liao, Derek S. Wang, Iskandar Sitdikov +3 more

Eromanga Adermann, Haiyue Kang, Martin Sevior +1 more

Imrane Chems Eddine Idrissi, Saïd Nouh, El Mehdi Bellfkih +2 more

The decoding of error-correcting codes (ECCs) is a critical aspect of communication systems, yet traditional decoding techniques can often be computationally demanding or ineffective for certain codes, necessitating innovative approaches. In this study, we introduce a hybrid approach that combines machine learning and automorphism techniques to optimize the decoding process. Specifically, we train multilayer perceptron (MLP) models to learn the mapping between error syndromes and their corresponding errors. While these models exhibit robust learning capabilities, their performance sometimes does not reach 100%. To mitigate this limitation, we exploit the automorphism group of the code—a set of structure-preserving transformations—to convert the errors that the MLP struggles to decode into ones it can process more effectively. We use a minimum number of p permutations, pre-calculating and storing all possible automorphisms to ensure computational efficiency. Our experimental results reveal that this hybrid approach substantially enhances the decoding performance of the MLP model, presenting a promising avenue for decoding ECCs. Importantly, this approach is not limited to MLP models and can be applied to any machine learning model with a learning score less than 100%, broadening its applicability and impact. By integrating machine learning with traditional algebraic coding theory, we propose a new paradigm that holds the potential to revolutionize the design of decoding systems, making them more efficient and effective.

Hiroshi Ohno

Imrane Chems Eddine Idrissi, Saïd Nouh, El Mehdi Bellfkih +2 more

Facing the challenge of enormous data sets variety, several machine learning-based algorithms for prediction (e.g, Support vector machine, multi layer perceptron and logistic regression) have been highly proposed and used over the last years in many fields. Error correcting codes (ECCs) are extensively used in practice to protect data against damaged data storage systems and against random errors due to noise effects. In this paper, we will use machine learning methods, especially multi-class logistic regression combined with the famous syndrome decoding algorithm. The main idea behind our decoding method which we call logistic regression decoder (LRDec) is to use the efficient multi-class logistic regression models to find errors from syndromes in linear codes such as bose, ray-chaudhuri and hocquenghem (BCH), and the quadratic residue (QR). Obtained results of the proposed decoder have a significant benefit in terms of bit error rate (BER) for random binary codes. The comparison of our decoder with many competitors proves its power. The proposed decoder has reached a success percentage of 100% for correctable errors in the studied codes.