Tomography of Quantum States from Structured Measurements via quantum-aware transformer
This work addresses the problem of accurately reconstructing quantum states for quantum computing researchers, offering an incremental improvement by incorporating measurement structure into the model.
The paper tackles quantum state tomography by proposing a quantum-aware transformer model that leverages the structure of quantum measurements, achieving high-fidelity reconstruction with robustness against experimental noise in simulations and on IBM quantum computers.
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.