# Experimental quantum homodyne tomography via machine learning

arXiv: https://arxiv.org/abs/1907.06589 · HTML: https://mlsanity.com/paper/1907.06589/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2019.

## Built on by (most cited first, 10 of 10)

- [Flexible learning of quantum states with generative query neural networks](https://mlsanity.com/paper/2202.06804/) (2022)
- [Quantum Similarity Testing with Convolutional Neural Networks](https://mlsanity.com/paper/2211.01668/) (2022)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Deep learning of quantum entanglement from incomplete measurements](https://mlsanity.com/paper/2205.01462/) (2022)
- [Mixed State Entanglement Classification using Artificial Neural Networks](https://mlsanity.com/paper/2102.06053/) (2021)
- [Quantum Pattern Recognition in Photonic Circuits](https://mlsanity.com/paper/2107.09961/) (2021)
- [Optical Quantum Mixed-State Reconstruction With Multiple Deep Learning Approaches](https://mlsanity.com/paper/2407.01734/) (2024)
- [Learning entanglement breakdown as a phase transition by confusion](https://mlsanity.com/paper/2202.00348/) (2022)
- [Dimension-adaptive machine-learning-based quantum state reconstruction](https://mlsanity.com/paper/2205.05804/) (2022)
- [Sequence-Model-Guided Measurement Selection for Quantum State Learning](https://mlsanity.com/paper/2507.09891/) (2025)

## Abstract (arXiv)

Complete characterization of states and processes that occur within quantum devices is crucial for understanding and testing their potential to outperform classical technologies for communications and computing. However, solving this task with current state-of-the-art techniques becomes unwieldy for large and complex quantum systems. Here we realize and experimentally demonstrate a method for complete characterization of a quantum harmonic oscillator based on an artificial neural network known as the restricted Boltzmann machine. We apply the method to optical homodyne tomography and show it to allow full estimation of quantum states based on a smaller amount of experimental data compared to state-of-the-art methods. We link this advantage to reduced overfitting. Although our experiment is in the optical domain, our method provides a way of exploring quantum resources in a broad class of large-scale physical systems, such as superconducting circuits, atomic and molecular ensembles, and optomechanical systems.