Neural decoders with permutation invariant structure

Bödeker, Lukas, Kusters, Luc J. B., Markus Müller

Xiangyu Chen, Min Ye

Neural decoders were introduced as a generalization of the classic Belief Propagation (BP) decoding algorithms, where the Trellis graph in the BP algorithm is viewed as a neural network, and the weights in the Trellis graph are optimized by training the neural network. In this work, we propose a novel neural decoder for cyclic codes by exploiting their cyclically invariant property. More precisely, we impose a shift invariant structure on the weights of our neural decoder so that any cyclic shift of inputs results in the same cyclic shift of outputs. Extensive simulations with BCH codes and punctured Reed-Muller (RM) codes show that our new decoder consistently outperforms previous neural decoders when decoding cyclic codes. Finally, we propose a list decoding procedure that can significantly reduce the decoding error probability for BCH codes and punctured RM codes. For certain high-rate codes, the gap between our list decoder and the Maximum Likelihood decoder is less than $0.1$dB. Code available at https://github.com/cyclicallyneuraldecoder/CyclicallyEquivariantNeuralDecoders

M Li, Wen Liu, Lei Shi +2 more

Graph neural networks (GNNs) have demonstrated strong capabilities in graph representation learning but still face limitations in efficiency and scalability. Quantum GNNs (QGNNs) offer a promising alternative. However, existing approaches often fail to fully exploit edge information, require substantial quantum resources, and insufficiently account for permutation invariance in graph learning. To address these challenges, this article proposes a permutation-invariant quantum GNN (PIQGNN). The proposed model introduces a low-qubit-cost quantum encoding strategy that jointly embeds node features, edge features, and graph topology into entangled quantum states using only $n$ qubits, where $n$ denotes the number of nodes, while explicitly enforcing permutation invariance. Furthermore, a symmetry-aware variational quantum neural network (QNN) is designed to enable end-to-end permutation-invariant learning. Its hyperparameters are optimized via Bayesian optimization to alleviate barren plateau (BP) effects and enhance training stability. Experimental results on multiple graph binary classification benchmark datasets demonstrate that, compared with classical GNNs, PIQGNN achieves competitive performance with a significantly reduced number of trainable parameters. Compared with existing QGNNs, PIQGNN attains higher accuracy with lower quantum resource requirements and exhibits stronger robustness under noisy conditions. These results indicate that PIQGNN provides an efficient, scalable, and noise-resilient quantum framework for graph learning, highlighting its practical potential in the noisy intermediate-scale quantum (NISQ) era.

Y.S. Balashov, S.N. Panychev, Marina Horoshaylova

Yingkai Ouyang

Quantum deletions, which are harder to correct than erasure errors, occur in many realistic settings. It is therefore pertinent to develop quantum coding schemes for quantum deletion channels. To date, not much is known about which explicit quantum error correction codes can combat quantum deletions. We note that any permutation-invariant quantum code that has a distance of$t+1$can correct$t$quantum deletions for any positive integer$t$in both the qubit and the qudit setting. Leveraging on coding properties of permutation-invariant quantum codes under erasure errors, we derive corresponding coding bounds for permutation-invariant quantum codes under quantum deletions. We focus our attention on a specific family of$N$-qubit permutation-invariant quantum codes, which we call shifted gnu codes. The main result of this work is that their encoding and decoding algorithms can be performed in$O(N)$and$O(N^{2})$.

Wang Ming, Yong Li, Jianqing Liu +3 more