# Demonstration of machine-learning-enhanced Bayesian quantum state estimation

arXiv: https://arxiv.org/abs/2212.08032 · HTML: https://mlsanity.com/paper/2212.08032/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 12 references that are in the map.
- First posted on arXiv 15 Dec 2022.

## Builds on (most cited first, 1 of 1)

- [Neural network state estimation for full quantum state tomography](https://mlsanity.com/paper/1811.06654/) (2018)

## Built on by (most cited first, 2 of 2)

- [Scalable bayesian shadow tomography for quantum property estimation with set transformers](https://mlsanity.com/paper/2509.18674/) (2025)
- [Fixed-Protocol Amortized MPS Tomography with Conformalized Predictive Uncertainty](https://mlsanity.com/paper/2607.11273/) (2026)

## Abstract (arXiv)

Machine learning (ML) has found broad applicability in quantum information science in topics as diverse as experimental design, state classification, and even studies on quantum foundations. Here, we experimentally realize an approach for defining custom prior distributions that are automatically tuned using ML for use with Bayesian quantum state estimation methods. Previously, researchers have looked to Bayesian quantum state tomography due to its unique advantages like natural uncertainty quantification, the return of reliable estimates under any measurement condition, and minimal mean-squared error. However, practical challenges related to long computation times and conceptual issues concerning how to incorporate prior knowledge most suitably can overshadow these benefits. Using both simulated and experimental measurement results, we demonstrate that ML-defined prior distributions reduce net convergence times and provide a natural way to incorporate both implicit and explicit information directly into the prior distribution. These results constitute a promising path toward practical implementations of Bayesian quantum state tomography.