  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.
