🤖 AI Summary
Traditional quantum state tomography (QST) methods neglect the structured quantum nature of measurements, limiting reconstruction accuracy and noise robustness. This work proposes the Quantum-Aware Transformer (QAT), the first Transformer architecture for QST that explicitly models the physical measurement-to-state mapping by embedding quantum operators as learnable query tokens. It further introduces the Bures distance as the loss function to directly optimize quantum state fidelity in an end-to-end manner. Evaluated on both numerical simulations and IBM’s real quantum hardware, QAT consistently outperforms classical QST approaches—achieving superior density matrix reconstruction accuracy and robustness under low-statistics sampling and noisy conditions. Key contributions are: (1) the first quantum-native Transformer architecture designed specifically for QST; (2) an operator-level learnable query mechanism; and (3) a Bures-geometry–driven, end-to-end fidelity optimization paradigm.
📝 Abstract
Quantum state tomography (QST) is the process of reconstructing the state of a quantum system (mathematically described as a density matrix) through a series of different measurements, which can be solved by learning a parameterized function to translate experimentally measured statistics into physical density matrices. However, the specific structure of quantum measurements for characterizing a quantum state has been neglected in previous work. In this paper, we explore the similarity between highly structured sentences in natural language and intrinsically structured measurements in QST. To fully leverage the intrinsic quantum characteristics involved in QST, we design a quantum-aware transformer (QAT) model to capture the complex relationship between measured frequencies and density matrices. In particular, we query quantum operators in the architecture to facilitate informative representations of quantum data and integrate the Bures distance into the loss function to evaluate quantum state fidelity, thereby enabling the reconstruction of quantum states from measured data with high fidelity. Extensive simulations and experiments (on IBM quantum computers) demonstrate the superiority of the QAT in reconstructing quantum states with favorable robustness against experimental noise.
