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Quantum state tomography (QST) is the process of reconstructing the state ofa quantum system (mathematically described as a density matrix) through aseries of different measurements, which can be solved by learning aparameterized function to translate experimentally measured statistics intophysical density matrices. However, the specific structure of quantummeasurements for characterizing a quantum state has been neglected in previouswork. In this paper, we explore the similarity between highly structuredsentences in natural language and intrinsically structured measurements in QST.To fully leverage the intrinsic quantum characteristics involved in QST, wedesign a quantum-aware transformer (QAT) model to capture the complexrelationship between measured frequencies and density matrices. In particular,we query quantum operators in the architecture to facilitate informativerepresentations of quantum data and integrate the Bures distance into the lossfunction to evaluate quantum state fidelity, thereby enabling thereconstruction of quantum states from measured data with high fidelity.Extensive simulations and experiments (on IBM quantum computers) demonstratethe superiority of the QAT in reconstructing quantum states with favorablerobustness against experimental noise.

Tomography of Quantum States from Structured Measurements via quantum-aware transformer