  With rapid progress across platforms for quantum systems, the problem of
many-body quantum state reconstruction for noisy quantum states becomes an
important challenge. Recent works found promise in recasting the problem of
quantum state reconstruction to learning the probability distribution of
quantum state measurement vectors using generative neural network models. Here
we propose the "Attention-based Quantum Tomography" (AQT), a quantum state
reconstruction using an attention mechanism-based generative network that
learns the mixed state density matrix of a noisy quantum state. The AQT is
based on the model proposed in "Attention is all you need" by Vishwani et al
(2017) that is designed to learn long-range correlations in natural language
sentences and thereby outperform previous natural language processing models.
We demonstrate not only that AQT outperforms earlier neural-network-based
quantum state reconstruction on identical tasks but that AQT can accurately
reconstruct the density matrix associated with a noisy quantum state
experimentally realized in an IBMQ quantum computer. We speculate the success
of the AQT stems from its ability to model quantum entanglement across the
entire quantum system much as the attention model for natural language
processing captures the correlations among words in a sentence.
