Formation of neural belief propagation decoders for quantum error correction codes

Two researchers from the University of Sherbrooke, Canada, have recently developed and trained belief-based neural decoders (BPs) for low-density low-density parity (LDPC) codes. Their study, described in an article published in Physical Review Letters, suggests that training can dramatically improve the performance of BP decoders, helping to solve the problems commonly associated with their application to quantum research.

"Ten years ago, I wrote an article with Yeojin Chung explaining how standard decoding algorithms for LDPC codes, widely used in classical communication, would fail in the quantum environment," David said. Poulin, one of the researchers who conducted the study, told Phys.org. "This problem has been haunting me ever since, recently we started to study the use of neural networks to decode quantum codes, but they all focused on one problem (decoding topological codes) that already contained a number of good man-made solutions was the perfect opportunity to revisit my favorite open problem and use neural networks to decode quantum codes without a previously known decoder. "

Although BP decoders are commonly used in a variety of contexts, they have so far proven unsuitable for decoding quantum error correction codes. This is due to a unique quantum feature called "error degeneracy", which basically means that there are several ways to correct an error in quantum parameters.

The classical BP algorithms consist of three simple equations. The structure of these equations allows an exact match with a network of feed-forward neurons. In other words, it is possible to reinterpret the BP equations commonly used to decode LDPC codes as describing the initial configuration of a neural network.

Previous research has shown that this "initial neural network" does not work well in quantum environments, despite higher performance than random neural networks. In their study, Poulin and his colleague Ye-Hua Liu improved the performance of the "initial neural network" by training it with data generated by numerical simulations.

"The training is guided by a target function that takes into account quantum effects," Liu told Phys.org. "In general, neural decoders have the advantage of adapting to arbitrary noise statistics in realistic channels, and our method is applicable to quantum LDPC codes without regular network structure." These codes are very promising for the realization of quantum low-time system error correction. "

The researchers found that training BP neural decoders using the adopted technique improved their performance for all families of LDPC codes tested. In addition, the training technique they used could help solve the degeneracy problem that typically affects the decoding of quantum LDPC codes.

"The formation of BP neural network can significantly improve its performance in quantum error correction, which means that a conventional algorithm can be adapted to quantum control by deep learning methods." "said Liu. "This prompts us to look for other examples like this one in quantum physics, in order to reveal a broader connection between in-depth learning and the natural sciences." For example, the spread of beliefs is largely used in many other areas of research, including statistical physics, which also implies beneficial for research in quantum statistical physics ".

In their future work, Poulin and Liu plan to study neuronal BP in the context of statistical physics. If researchers follow training using the same technique, researchers expect BP, also called "cavity method" in this particular context, to also show improved performance in this context.

"More generally, belief propagation belongs to the important class of message-transmission algorithms, which are found to be closely related to graph convolution networks in deep learning research," Liu added. "It would be very successful to better understand these structures from the point of view of a physicist."

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