Quantum Error Correction (QEC) is one of the fundamental problems in quantum computer systems, which aims to detect and correct errors in the data qubits within quantum computers. Due to the presence of unreliable data qubits in existing quantum computers, implementing quantum error correction is a critical step when establishing a stable quantum computer system. Recently, machine learning (ML)-based approaches have been proposed to address this challenge. However, they lack a thorough understanding of quantum error correction. To bridge this research gap, we provide a new perspective to understand machine learning-based QEC in this paper. We find that syndromes in the ancilla qubits result from errors on connected data qubits, and distant ancilla qubits can provide auxiliary information to rule out some incorrect predictions for the data qubits. Therefore, to detect errors in data qubits, we must consider the information present in the long-range ancilla qubits. To the best of our knowledge, machine learning is less explored in the dependency relationship of QEC. To fill the blank, we curate a machine learning benchmark to assess the capacity to capture long-range dependencies for quantum error correction. To provide a comprehensive evaluation, we evaluate seven state-of-the-art deep learning algorithms spanning diverse neural network architectures, such as convolutional neural networks, graph neural networks, and graph transformers. Our exhaustive experiments reveal an enlightening trend: By enlarging the receptive field to exploit information from distant ancilla qubits, the accuracy of QEC significantly improves. For instance, U-Net can improve CNN by a margin of about 50%. Finally, we provide a comprehensive analysis that could inspire future research in this field.
Quantum Error Correction (QEC) is one of the fundamental problems in quantum computer systems, which aims to detect and correct errors in the data qubits within quantum computers. Due to the presence of unreliable data qubits in existing quantum computers, implementing quantum error correction is a critical step when establishing a stable quantum computer system. Recently, machine learning (ML)-based approaches have been proposed to address this challenge. However, they lack a thorough understanding of quantum error correction. To bridge this research gap, we provide a new perspective to understand machine learning-based QEC in this paper. We find that syndromes in the ancilla qubits result from errors on connected data qubits, and distant ancilla qubits can provide auxiliary information to rule out some incorrect predictions for the data qubits. Therefore, to detect errors in data qubits, we must consider the information present in the long-range ancilla qubits. To the best of our knowledge, machine learning is less explored in the dependency relationship of QEC. To fill the blank, we curate a machine learning benchmark to assess the capacity to capture long-range dependencies for quantum error correction. To provide a comprehensive evaluation, we evaluate seven state-of-the-art deep learning algorithms spanning diverse neural network architectures, such as convolutional neural networks, graph neural networks, and graph transformers. Our exhaustive experiments reveal an enlightening trend: By enlarging the receptive field to exploit information from distant ancilla qubits, the accuracy of QEC significantly improves. For instance, U-Net can improve CNN by a margin of about 50%. Finally, we provide a comprehensive analysis that could inspire future research in this field.
Quantum Error Correction (QEC) is the process of detecting and correcting errors in quantum systems, which are prone to decoherence and quantum noise. QEC is crucial for developing stable and highly accurate quantum computing systems, therefore, several research efforts have been made to develop the best QEC strategy. Recently, Google's breakthrough shows great potential to improve the accuracy of the existing error correction methods. This survey provides a comprehensive review of advancements in the use of artificial intelligence (AI) tools to enhance QEC schemes for existing Noisy Intermediate Scale Quantum (NISQ) systems. Specifically, we focus on machine learning (ML) strategies and span from unsupervised, supervised, semi-supervised, to reinforcement learning methods. It is clear from the evidence, that these methods have recently shown superior efficiency and accuracy in the QEC pipeline compared to conventional approaches. Our review covers more than 150 relevant studies, offering a comprehensive overview of progress and perspective in this field. We organized the reviewed literature on the basis of the AI strategies employed and improvements in error correction performance. We also discuss challenges ahead such as data sparsity caused by limited quantum error datasets and scalability issues as the number of quantum bits (qubits) in quantum systems kept increasing very fast. We conclude the paper with summary of existing works and future research directions aimed at deeper integration of AI techniques into QEC strategies.
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.
Abstract Quantum machine learning (QML) is an emerging field that promises advantages such as faster training, improved reliability and superior feature extraction over classical counterparts. However, its implementation on quantum hardware is challenging due to the noise inherent in these systems, necessitating the use of quantum error correction (QEC) codes. Current QML research remains primarily theoretical, often assuming noise-free environments and offering little insight into the integration of QEC with QML implementations. To address this, we investigate the performance of a simple, parity-classifying Variational Quantum Classifier (VQC) implemented with the [[4,2,2]] error-detecting stabiliser code in a simulated noisy environment. To our knowledge, this is the first implementation of a stabiliser-based error detection code to a QML algorithm. We invoke ancilla qubits to logically encode rotation gates, and classically simulate the logically-encoded VQC under two simple noise models representing gate noise and environmental noise. We demonstrate that the stabiliser code improves the training accuracy at convergence compared to noisy implementations without error detection. However, we find that the effectiveness and reliability of error detection is contingent upon keeping the ancilla qubit error rates below a specific threshold, due to the propagation of ancilla errors to the physical qubits. Our results provide an important insight that extends to QML implemented with full error-correction: when the QEC code requires ancilla qubits for logical rotations but cannot fully correct errors propagated between ancilla and physical qubits, the maximum achievable accuracy of the QML model is constrained. This highlights the need for additional error correction or mitigation strategies to support the practical implementation of QML algorithms with QEC on quantum devices.
Quantum error correction (QEC) is critical for the reliable implementation of quantum computers, but current QEC protocols often rely on fixed parameters and struggle to adapt to fluctuating environmental noise. This work proposes a novel approach to QEC that leverages machine learning (ML) to dynamically adapt the parameters of QEC protocols in real-time. The core idea involves training neural networks to predict error rates based on observed quantum data and subsequently optimizing the error correction strategies. This adaptive framework offers the potential for significantly improved performance and resilience against evolving noise characteristics. The primary focus is on the theoretical framework and algorithm design, without the need for experimental validation. The proposed method represents a shift from static QEC to a more flexible and efficient system, addressing a key limitation in current quantum computing architectures. The key concept is represented by the following equation: εt = f(xt, θt, η), where εt is the error rate at time *t*, xt is the quantum state at time *t*, θt are the parameters of the QEC protocol at time *t*, and η is the learning rate. This equation highlights the adaptive nature of the system. The efficiency of the system is measured by the reduction in error rates achieved through adaptive parameter adjustment. Further analysis includes the concept of a cost function, C(θ), that represents the overall error correction performance. The goal is to minimize this cost function using the trained neural network. The core of the system relies on a feedback loop – the neural network predicts the error rate, which then influences the adjustment of the QEC protocol parameters.
Quantum computing has the potential to solve problems that are intractable for classical systems, yet the high error rates in contemporary quantum devices often exceed tolerable limits for useful algorithm execution. Quantum Error Correction (QEC) mitigates this by employing redundancy, distributing quantum information across multiple data qubits and utilizing syndrome qubits to monitor their states for errors. The syndromes are subsequently interpreted by a decoding algorithm to identify and correct errors in the data qubits. This task is complex due to the multiplicity of error sources affecting both data and syndrome qubits as well as syndrome extraction operations. Additionally, identical syndromes can emanate from different error sources, necessitating a decoding algorithm that evaluates syndromes collectively. Although machine learning (ML) decoders such as multi-layer perceptrons (MLPs) and convolutional neural networks (CNNs) have been proposed, they often focus on local syndrome regions and require retraining when adjusting for different code distances. We introduce a transformer-based QEC decoder which employs self-attention to achieve a global receptive field across all input syndromes. It incorporates a mixed loss training approach, combining both local physical error and global parity label losses. Moreover, the transformer architecture's inherent adaptability to variable-length inputs allows for efficient transfer learning, enabling the decoder to adapt to varying code distances without retraining. Evaluation on six code distances and ten different error configurations demonstrates that our model consistently outperforms non-ML decoders, such as Union Find (UF) and Minimum Weight Perfect Matching (MWPM), and other ML decoders, thereby achieving best logical error rates. Moreover, the transfer learning can save over 10x of training cost.
Quantum error correction (QEC) is the most promising route toward fault-tolerant quantum computing and, thus, useful quantum computers. QEC operates as a continuous measure-decode-correct cycle: ancilla qubits are read out, a decoder infers errors from the resulting syndromes, and corrections are applied before the next round begins. Within this loop, readout occupies a uniquely critical role, as it is the sole source of ground truth available to the decoder. Yet readout is also the slowest and most error-prone operation in the stack, with characteristics that vary across qubits and drift over time; This complexity propagates directly to the classical control hardware, and in particular to the FPGA-hosted machine-learning (ML) discriminator that must classify each analog signal into a binary syndrome outcome. Despite this central role, QEC performance has not yet been studied in depth from the perspective of readout characteristics, readout length, and their co-design with an ML discriminator.
We introduce Oraqle, an end-to-end benchmarking framework that evaluates qubit-state readout and its impact on QEC performance across real experimentally extracted qubit-state-readout datasets, state-of-the-art ML discriminators, multiple QEC codes, and hardware regimes spanning current to projected devices. Our study reveals three asymmetric findings: The measurement duration can be significantly reduced with nearly no penalty to the logical error rate; The discriminator complexity barely affects the QEC performance, as residual errors are written into device physics rather than the model; and the impact of qubit-state readout on the logical error rate is conditional on where the hardware sits in the QEC landscape, a window that widens as devices mature.