Attention to complexity II: Attention based quantum decoder

With the promising development of quantum computers comes a natural necessity of storing quantum information, which can be itself a challenging task due to the omnipresence of noise induced errors in quantum devices. Quantum error-correcting codes aim to combat this issue by encoding logical qubits in the state space of a large number of physical qubits, so that within a certain threshold of noise strength, faithful reconstruction of the stored logical qubit is still possible. However, the decoding scheme often depends on specific quantum code and noise models, making it a challenging task in practice. Using the machinery of the quantum attention networks (QAN),we study the phase diagram of error correcting codes, under coherent and incoherent perturbations. We find the network learns to identify the error-protected, long-range-entangled phase, by acting as an effective neural-network based decoder that importance-samples snapshots of the physical qubits by assigning higher attention scores to uncorrupted snapshots largely inside the code space. Our method shows that within a certain threshold of noise strength, the QAN successfully identifies the states in the code space of a two-dimensional toric code. Our work paves the way towards machine-learning based decoder in more general noisy quantum error-correcting codes.