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.
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.
Quantum error-correcting codes are essential for achieving fault-tolerant quantum computing. Heavy hexagonal code is a type of topological code that leverages the arrangement of qubits to find and correct errors. The heavy hexagonal code is suitable for superconducting architectures, specifically graph layouts with a limited number of connections. The topological error correction methods work well, but they need more qubits, cannot be used for different sizes of quantum systems, are less reliable, and do not work well with changing quantum distributions. Thus, the research proposes an Ardea-guided exploit optimized sparse-dual attention enabled meta-learning-based convolutional neural network with bi-directional long short-term memory model (AGuESD-MCBiTM). The method exhibits effective correction over dynamic environments with the utilization of meta-learning and the extraction of statistical information, which provides a detailed representation of the qubit patterns. The Ardea-guided exploit optimized (AGuEO) algorithm tunes the weights of MCBiTM and acquires optimal solutions with higher convergence. Moreover, the sparse-dual attention module and meta-learning-based MCBiTM model, which together provide scalable, real-time identification of non-linear qubit noise fluctuations with lower computational cost. Comparatively, the proposed AGuESD-MCBiTM exhibits superior error correction with a higher correlation of 0.97, accuracy of 98.93%, and R-squared value of 0.93, as well as a lower Root mean square error of 1.87, Mean absolute error of 1.20, Bit error rate of 1.85, Logical error rate of 3.82, and mean square error of 3.49 in circuit 2, respectively.
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.
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.
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.
Abstract To address qubits' high environmental sensitivity and reduce the significant error rates in current quantum devices, quantum error correction stands as one of the most dependable approaches. The topological surface code, renowned for its unique qubit lattice structure, is widely considered a pivotal tool for enabling fault-tolerant quantum computation. Through redundancy introduced across multiple qubits, the surface code safeguards quantum information and identifies errors via state changes captured by syndrome qubits. However, simultaneous errors in data and syndrome qubits substantially escalate decoding complexity. Quantum Generative Adversarial Networks (QGANs) have emerged as promising deep learning frameworks, effectively harnessing quantum advantages for practical tasks such as image processing and data optimization. Consequently, a topological code trainer for quantum-classical hybrid GANs is proposed as an auxiliary model to enhance error correction in machine learning-based decoders, demonstrating significantly improved training accuracy compared to the traditional Minimum Weight Perfect Matching (MWPM) algorithm, which achieves an accuracy of 65 . Numerical experiments reveal that the decoder achieves a fidelity threshold of P=0.1978, substantially surpassing the traditional algorithm's threshold of P=0.1024. To enhance decoding efficiency, a Transformer decoder is integrated, incorporating syndrome error outputs trained via QGANs into its framework. By leveraging its self-attention mechanism, the Transformer effectively captures long-range qubit dependencies at a global scale, enabling high-fidelity error correction over larger dimensions. Numerical validation of the surface code error threshold demonstrates an 8.5 threshold with a correction success rate exceeding 94, whereas the local MWPM decoder achieves only 55 and fails to support large-scale computation at a 4 threshold.
A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error correction. Here we show that a recurrent neural network can be trained, using only experimentally accessible data, to detect errors in a widely used topological code, the surface code, with a performance above that of the established minimum-weight perfect matching (or blossom) decoder. The performance gain is achieved because the neural network decoder can detect correlations between bit-flip (X) and phase-flip (Z) errors. The machine learning algorithm adapts to the physical system, hence no noise model is needed. The long short-term memory layers of the recurrent neural network maintain their performance over a large number of quantum error correction cycles, making it a practical decoder for forthcoming experimental realizations of the surface code.