# Experimental neural network enhanced quantum tomography

arXiv: https://arxiv.org/abs/1904.05902 · HTML: https://mlsanity.com/paper/1904.05902/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2019.

## Built on by (most cited first, 18 of 18)

- [Flexible learning of quantum states with generative query neural networks](https://mlsanity.com/paper/2202.06804/) (2022)
- [Deep learning of quantum entanglement from incomplete measurements](https://mlsanity.com/paper/2205.01462/) (2022)
- [Multimodal deep representation learning for quantum cross-platform verification](https://mlsanity.com/paper/2311.03713/) (2023)
- [Tomography of Quantum States from Structured Measurements via quantum-aware transformer](https://mlsanity.com/paper/2305.05433/) (2023)
- [Exponentially improved efficient machine learning for quantum many-body states with provable guarantees](https://mlsanity.com/paper/2304.04353/) (2023)
- [Gradient-descent quantum process tomography by learning Kraus operators](https://mlsanity.com/paper/2208.00812/) (2022)
- [Quantum Pattern Recognition in Photonic Circuits](https://mlsanity.com/paper/2107.09961/) (2021)
- [Estimating the Euclidean quantum propagator with deep generative modeling of Feynman paths](https://mlsanity.com/paper/2202.02750/) (2022)
- [Optical Quantum Mixed-State Reconstruction With Multiple Deep Learning Approaches](https://mlsanity.com/paper/2407.01734/) (2024)
- [Dimension-adaptive machine-learning-based quantum state reconstruction](https://mlsanity.com/paper/2205.05804/) (2022)
- [Quantum-machine-learning channel discrimination](https://mlsanity.com/paper/2206.09933/) (2022)
- [Fast Minimization of Expected Logarithmic Loss via Stochastic Dual Averaging](https://mlsanity.com/paper/2311.02557/) (2023)
- [Reinforcement learning to learn quantum states for Heisenberg scaling accuracy](https://mlsanity.com/paper/2412.02334/) (2024)
- [Regression of high dimensional angular momentum states of light](https://mlsanity.com/paper/2206.09873/) (2022)
- [Learning Informative Latent Representation for Quantum State Tomography](https://mlsanity.com/paper/2310.00518/) (2023)
- [Optical Quantum Sensing for Agnostic Environments via Deep Learning](https://mlsanity.com/paper/2311.07203/) (2023)
- [Entanglement Detection with Quantum-inspired Kernels and SVMs](https://mlsanity.com/paper/2508.17909/) (2025)
- [Noise-Robust Quantum State Characterization for Remote State Preparation with Deep Learning](https://mlsanity.com/paper/2609.20523/) (2026)

## Abstract (arXiv)

Quantum tomography is currently ubiquitous for testing any implementation of a quantum information processing device. Various sophisticated procedures for state and process reconstruction from measured data are well developed and benefit from precise knowledge of the model describing state preparation and the measurement apparatus. However, physical models suffer from intrinsic limitations as actual measurement operators and trial states cannot be known precisely. This scenario inevitably leads to state-preparation-and-measurement (SPAM) errors degrading reconstruction performance. Here we develop and experimentally implement a machine learning based protocol reducing SPAM errors. We trained a supervised neural network to filter the experimental data and hence uncovered salient patterns that characterize the measurement probabilities for the original state and the ideal experimental apparatus free from SPAM errors. We compared the neural network state reconstruction protocol with a protocol treating SPAM errors by process tomography, as well as to a SPAM-agnostic protocol with idealized measurements. The average reconstruction fidelity is shown to be enhanced by 10% and 27%, respectively. The presented methods apply to the vast range of quantum experiments which rely on tomography.