Machine Learning Enhanced Quantum State Tomography: A Covariance Matrix Approach

Juan Camilo Rodriguez Perez^1*, Hsien-Yi Hsieh¹, Ray-Kuang Lee^1,2

¹Institute of Photonics Technology (IPT), National Tsing Hua University, Hsinchu, Taiwan
²Department of Physics, National Tsing Hua University, Hsinchu, Taiwan

* Presenter:Juan Camilo Rodriguez Perez, email:jcrodriguezpj@gapp.nthu.edu.tw

We propose a machine learning-enhanced approach to quantum state tomography, focusing on the efficient reconstruction of quantum optical states via the covariance matrix representation. Density matrix-based tomography faces challenges in scalability and precision, particularly in high-dimensional Fock representation, while this problem is more manageable for single-mode states, it becomes significantly more challenging for two-mode states. Our model leverages homodyne detection data, using quadrature sequences as input to predict the covariance matrix of single- and two-mode squeezed states. This approach enables the precise estimation of essential quantum properties, including purity, squeezing, and anti-squeezing levels. The lightweight architecture ensures computational efficiency, enabling real-time reconstruction of quantum states. We validate our model against simulated and experimental data, demonstrating superior performance in the presence of both single- and two-mode squeezed Gaussian states, as well as multimodal mixtures. The model also shows promise for the tomography of entangled states, paving the way for its application in quantum information protocols. Covariance matrix reconstruction represents a significant step towards more efficient quantum state characterization for single- and two-mode states, keeping high precision levels and demonstrating robustness against multimode noise sources.

Keywords: Quantum State Tomography, Machine Learning, Covariance Matrix, Squeezed States, Entangled states