# Flexible learning of quantum states with generative query neural networks

arXiv: https://arxiv.org/abs/2202.06804 · HTML: https://mlsanity.com/paper/2202.06804/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 58 references that are in the map.
- First posted on arXiv 14 Feb 2022.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Quantum State Tomography with Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2008.03240/) (2020)
- [Online Learning of Quantum States](https://mlsanity.com/paper/1802.09025/) (2018)
- [Quantum statistical query learning](https://mlsanity.com/paper/2002.08240/) (2020)
- [Experimental neural network enhanced quantum tomography](https://mlsanity.com/paper/1904.05902/) (2019)
- [Learning hard quantum distributions with variational autoencoders](https://mlsanity.com/paper/1710.00725/) (2017)
- [Classification and reconstruction of optical quantum states with deep neural networks](https://mlsanity.com/paper/2012.02185/) (2020)
- [Adaptive Quantum State Tomography with Neural Networks](https://mlsanity.com/paper/1812.06693/) (2018)
- [Efficient Quantum State Sample Tomography with Basis-dependent Neural-networks](https://mlsanity.com/paper/2009.07601/) (2020)
- [Experimental quantum homodyne tomography via machine learning](https://mlsanity.com/paper/1907.06589/) (2019)
- [Neural network state estimation for full quantum state tomography](https://mlsanity.com/paper/1811.06654/) (2018)

## Built on by (most cited first, 16 of 16)

- [Quantum Similarity Testing with Convolutional Neural Networks](https://mlsanity.com/paper/2211.01668/) (2022)
- [Explainable Representation Learning of Small Quantum States](https://mlsanity.com/paper/2306.05694/) (2023)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Tomography of Quantum States from Structured Measurements via quantum-aware transformer](https://mlsanity.com/paper/2305.05433/) (2023)
- [ShadowNet for Data-Centric Quantum System Learning](https://mlsanity.com/paper/2308.11290/) (2023)
- [Learning quantum properties from short-range correlations using multi-task networks](https://mlsanity.com/paper/2310.11807/) (2023)
- [Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits](https://mlsanity.com/paper/2408.12199/) (2024)
- [Rethink the Role of Deep Learning towards Large-scale Quantum Systems](https://mlsanity.com/paper/2505.13852/) (2025)
- [Noise-Agnostic Quantum Error Mitigation with Data Augmented Neural Models](https://mlsanity.com/paper/2311.01727/) (2023)
- [Demonstration of Efficient Predictive Surrogates for Large-scale Quantum Processors](https://mlsanity.com/paper/2507.17470/) (2025)
- [TriQXNet: Forecasting Dst Index from Solar Wind Data Using an Interpretable Parallel Classical-Quantum Framework with Uncertainty Quantification](https://mlsanity.com/paper/2407.06658/) (2024)
- [Sequence-Model-Guided Measurement Selection for Quantum State Learning](https://mlsanity.com/paper/2507.09891/) (2025)
- [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)
- [Sample-efficient quantum error mitigation via classical learning surrogates](https://mlsanity.com/paper/2511.07092/) (2025)
- [GRPO-QPS: Target-Preserving Reinforcement Learning for Quantum Posterior Sampling](https://mlsanity.com/paper/2609.14711/) (2026)

## Abstract (arXiv)

Deep neural networks are a powerful tool for the characterization of quantum states. Existing networks are typically trained with experimental data gathered from the specific quantum state that needs to be characterized. But is it possible to train a neural network offline and to make predictions about quantum states other than the ones used for the training? Here we introduce a model of network that can be trained with classically simulated data from a fiducial set of states and measurements, and can later be used to characterize quantum states that share structural similarities with the states in the fiducial set. With little guidance of quantum physics, the network builds its own data-driven representation of quantum states, and then uses it to predict the outcome statistics of quantum measurements that have not been performed yet. The state representation produced by the network can also be used for tasks beyond the prediction of outcome statistics, including clustering of quantum states and identification of different phases of matter. Our network model provides a flexible approach that can be applied to online learning scenarios, where predictions must be generated as soon as experimental data become available, and to blind learning scenarios where the learner has only access to an encrypted description of the quantum hardware.