Topological quantum error-correcting codes are an important tool for realizing fault-tolerant quantum computers. Heavy hexagonal coding is a new class of quantum error-correcting coding that assigns physical and auxiliary qubits to the vertices and edges of a low-degree graph. The layout of heavy hexagonal codes is particularly suitable for superconducting qubit architectures to reduce frequency conflicts and crosstalk. Although various topological code decoders have been proposed, constructing the optimal decoder remains challenging. Machine learning is an effective decoding scheme for topological codes, and in this paper, we propose a machine learning heavy hexagonal decoder based on a convolutional neural network (CNN) to obtain the decoding threshold. We test our method on heavy hexagonal codes with code distance of three, five, and seven, and increase it to five, seven, and nine by optimizing the RestNet network architecture. Our results show that the decoder thresholding accuracies are about 0.57% and 0.65%, respectively, which are about 25% higher than the conventional decoding scheme under the depolarizing noise model. The proposed decoding architecture is also applicable to other topological code families.
Topological quantum error-correcting codes are an important tool for realizing fault-tolerant quantum computers. Heavy hexagonal coding is a new class of quantum error-correcting coding that assigns physical and auxiliary qubits to the vertices and edges of a low-degree graph. The layout of heavy hexagonal codes is particularly suitable for superconducting qubit architectures to reduce frequency conflicts and crosstalk. Although various topological code decoders have been proposed, constructing the optimal decoder remains challenging. Machine learning is an effective decoding scheme for topological codes, and in this paper, we propose a machine learning heavy hexagonal decoder based on a convolutional neural network (CNN) to obtain the decoding threshold. We test our method on heavy hexagonal codes with code distance of three, five, and seven, and increase it to five, seven, and nine by optimizing the RestNet network architecture. Our results show that the decoder thresholding accuracies are about 0.57% and 0.65%, respectively, which are about 25% higher than the conventional decoding scheme under the depolarizing noise model. The proposed decoding architecture is also applicable to other topological code families.
Decoding error syndromes for topological quantum error correcting codes, such as surface and heavy hexagonal codes, is computationally expensive. While minimum weight perfect matching (MWPM) algorithms have been commonly used for decoding, recent works have demonstrated the efficacy of machine learning (ML), particularly neural networks, in decoding syndromes for these codes. In this study, we introduce a ML-based decoder tailored to heavy hexagonal code to address asymmetric noise channels which reflect real-world scenario better than the depolarization model considered in previous works. Our proposed decoder shows∼5×and∼22×improvements in the threshold values for amplitude and amplitude-phase damping noise models respectively over MWPM methods. Our decoder is also robust to changes in asymmetry, with the threshold reducing by only ~ 3.6% for a10×change in asymmetry.
Abstract The error correction model’s main purpose in heavy hexagonal quantum codes is to improve their reliability for quantum computing applications. Existing challenges include finding the optimal decoder for quantum error correction in heavy hexagonal codes. This research propels the frontier of quantum error correction, with a specific focus on tailoring topological quantum error-correcting codes for the unique challenges posed by superconducting qubits in quantum computers. In response, this research harnesses the power of deep learning, presenting a Humming sparrow optimization based self-adaptive deep CNN (HSO-based SADCNN) model designed for heavy hexagonal codes. This decoder incorporates a Self-adaptive Deep CNN (SADCNN) Noise Correction Module, a sophisticated component to refine error correction. The proposed decoder’s efficacy is rigorously evaluated across varying code distances (three, five, and seven) using the Humming Sparrow Optimization (HSO) algorithm. HSO, intricately designed to fine-tune the SADCNN decoder, significantly enhances its error correction capabilities for heavy hexagonal quantum codes. The algorithm seamlessly integrates advantageous characteristics of herding and tracing from Humming Bird optimization and Sparrow search optimization, representing a critical stride in advancing the reliability of quantum computing applications, particularly within the intricate domain of heavy hexagonal quantum codes. Based upon the achievements, the Training Percentage (TP) 90 metrics demonstrate significant progress, boasting a commendable accuracy of 97.35% 97.35 % , coupled with reduced logical error probability and a diminished bit error rate, marked at 5.51 and 3.72, respectively.
Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers. In order to find the best syndrome of the stabilizer code in quantum error correction, we need to find a fast and close to the optimal threshold decoder. In this work, we build a convolutional neural network (CNN) decoder to correct errors in the toric code based on the system research of machine learning. We analyze and optimize various conditions that affect CNN, and use the RestNet network architecture to reduce the running time. It is shortened by 30%–40%, and we finally design an optimized algorithm for CNN decoder. In this way, the threshold accuracy of the neural network decoder is made to reach 10.8%, which is closer to the optimal threshold of about 11%.The previous threshold of 8.9%–10.3% has been slightly improved, and there is no need to verify the basic noise.
Decoding is an essential component of quantum error correction (QEC), translating stabilizer measurement outcomes into corrective actions that suppress logical errors and preserve logical quantum information. Building fault-tolerant architectures requires increasing the code distance, which in turn places growing demands on decoding accuracy, scalability, and practical deployability. While a wide range of decoding algorithms have been proposed and demonstrated, achieving reliable, scalable, and real-time decoding remains a significant challenge. Machine-learning (ML) approaches are particularly well suited to this setting, as quantum error decoding is fundamentally a problem of processing large volumes of classical data with complex spatiotemporal correlations. This chapter surveys ML-based methods for quantum error decoding, with a focus on topological codes and an emphasis on architectural principles, practical performance, and real-time considerations. We first frame decoding as a learning problem and outline key paradigms, including discriminative, generative, and reinforcement-learning formulations. We then introduce the neural network building blocks that underpin most contemporary neural decoders and discuss how these components can be integrated to balance expressivity, scalability, and latency. Building on this architectural perspective, we review recent progress and benchmarks in neural decoding for memory experiments, and discuss real-time decoding, open challenges, and future directions toward scalable fault-tolerant quantum computing.
Heavy hexagonal coding is a type of quantum error-correcting coding in which the edges and vertices of a low-degree graph are assigned auxiliary and physical qubits. While many topological code decoders have been presented, it is still difficult to construct the optimal decoder due to leakage errors and qubit collision. Therefore, this research proposes a Re-locative Guided Search optimized self-sparse attention-enabled convolutional Neural Network with Long Short-Term Memory (RlGS2-DCNTM) for performing effective error correction in quantum codes. The integration of the self-sparse attention mechanism in the proposed model increases the feature learning ability of the model to selectively focus on informative regions of the input codes. In addition, the use of statistical features computes the statistical properties of the input, thus aiding the model to perform complex tasks effectively. For model tuning, this research utilizes the RIGS nature-inspired algorithm that mimics the re-locative, foraging, and hunting strategies, which avoids local optima problems and improves the convergence speed of the RlGS2-DCNTM for Quantum error correction. When compared with other methods, the proposed RlGS2-DCNTM algorithm offers superior efficacy with a Minimum Mean Squared Error (MSE) of 4.26, Root Mean Squared Error of 2.06, Mean Absolute Error of 1.14 and a maximum correlation and [Formula: see text] of 0.96 and 0.92 respectively, which shows that the proposed model is highly suitable for real-time error decoding tasks.
To perform reliable information processing in quantum computers, quantum error-correction (QEC) codes are essential for the detection and correction of errors in the qubits. Among QEC codes, topological QEC codes are designed to interact between the neighboring qubits, which is a promising property for easing the implementation requirements. In addition, the locality to the qubits provides unusual tolerance to local errors. Recently, various decoding algorithms based on machine learning have been proposed to improve the decoding performance and latency of QEC codes. In this work, we propose a new decoding algorithm for surface codes, i.e., a type of topological codes, by using convolutional neural networks (CNN) tailored for the topological lattice structure of the surface codes. In particular, the proposed algorithm takes advantage of the syndrome pattern which is represented as a part of a rectangular lattice given to the CNN as its input. The remaining part of the rectangular lattice is filled with a carefully selected incoherent value for better logical error-rate performance. In addition, we introduce how to optimize the hyper-parameters in the CNN, according to the lattice structure of a given surface code. This reduces the overall decoding complexity and makes the CNN-based decoder computationally more suitable for implementation. The numerical results show that the proposed decoding algorithm effectively improves the decoding performance in terms of logical error-rate as compared to the existing algorithms, on various quantum error models.