Machine learning for quantum state tomography: robust covariance matrix estimation for squeezed vacuum states with...

Area of Science:

• Quantum optics
• Machine learning
• Quantum information science

Background:

• Characterizing quantum states is crucial for quantum technologies.
• Traditional methods like density matrix reconstruction are computationally intensive.
• Gaussian quantum states are fundamental building blocks in quantum information processing.

Purpose of the Study:

• To develop a fast and accurate method for estimating the covariance matrix of noisy Gaussian quantum states.
• To reconstruct impure squeezed vacuum states using sparse measurements.
• To provide a lightweight representation for lab-generated Gaussian states.

Main Methods:

• Utilized supervised machine learning with convolutional neural networks.
• Employed a model mixing thermal and squeezed thermal states.
• Reconstructed states from sparse measurements of quadrature sequences.

Main Results:

• Achieved high fidelity and precision in covariance matrix estimation, even at high squeezing levels.
• Demonstrated accuracy by benchmarking against experimental data of squeezed vacuum states.
• Quantified experimental degradation and verified robustness to thermal noise.

Conclusions:

• The machine learning method offers an efficient alternative to traditional state tomography.
• The approach accurately characterizes Gaussian quantum states and their noise-induced degradation.
• Laid the foundation for real-time quantum state tomography of multi-component and multi-mode Gaussian states.