# Tomography of Quantum States from Structured Measurements via quantum-aware transformer

arXiv: https://arxiv.org/abs/2305.05433 · HTML: https://mlsanity.com/paper/2305.05433/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 74 references that are in the map.
- First posted on arXiv 9 May 2023.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [SpAtten: Efficient Sparse Attention Architecture with Cascade Token and Head Pruning](https://mlsanity.com/paper/2012.09852/) (2020)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Learned Token Pruning for Transformers](https://mlsanity.com/paper/2107.00910/) (2021)
- [Quantum State Tomography with Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2008.03240/) (2020)
- [Attention-based Quantum Tomography](https://mlsanity.com/paper/2006.12469/) (2020)
- [Experimental neural network enhanced quantum tomography](https://mlsanity.com/paper/1904.05902/) (2019)
- [Flexible learning of quantum states with generative query neural networks](https://mlsanity.com/paper/2202.06804/) (2022)
- [Machine learning assisted quantum state estimation](https://mlsanity.com/paper/2003.03441/) (2020)
- [Fidelity-based Probabilistic Q-learning for Control of Quantum Systems](https://mlsanity.com/paper/1806.03145/) (2018)
- [Neural network state estimation for full quantum state tomography](https://mlsanity.com/paper/1811.06654/) (2018)
- [On compression rate of quantum autoencoders: Control design, numerical and experimental realization](https://mlsanity.com/paper/2005.11149/) (2020)
- [Learning-based Quantum Robust Control: Algorithm, Applications and Experiments](https://mlsanity.com/paper/1702.03946/) (2017)
- [On the experimental feasibility of quantum state reconstruction via machine learning](https://mlsanity.com/paper/2012.09432/) (2020)
- [Curriculum-based Deep Reinforcement Learning for Quantum Control](https://mlsanity.com/paper/2012.15427/) (2020)
- [Neural networks for quantum state tomography with constrained measurements](https://mlsanity.com/paper/2111.09504/) (2021)
- [Quantum estimation, control and learning: opportunities and challenges](https://mlsanity.com/paper/2201.05835/) (2022)
- [Quantum Ensemble Classification: A Sampling-based Learning Control Approach](https://mlsanity.com/paper/1312.6945/) (2013)
- [Dimension-adaptive machine-learning-based quantum state reconstruction](https://mlsanity.com/paper/2205.05804/) (2022)
- [Auxiliary Task-based Deep Reinforcement Learning for Quantum Control](https://mlsanity.com/paper/2302.14312/) (2023)
- [Two-stage Estimation for Quantum Detector Tomography: Error Analysis, Numerical and Experimental Results](https://mlsanity.com/paper/1905.05323/) (2019)
- [Hybrid filtering for a class of nonlinear quantum systems subject to classical stochastic disturbances](https://mlsanity.com/paper/2004.07050/) (2020)

## Built on by (most cited first, 8 of 8)

- [ShadowNet for Data-Centric Quantum System Learning](https://mlsanity.com/paper/2308.11290/) (2023)
- [On the Convergence of Gradient Descent on Learning Transformers with Residual Connections](https://mlsanity.com/paper/2506.05249/) (2025)
- [Quantum Adjoint Convolutional Layers for Effective Data Representation](https://mlsanity.com/paper/2404.17378/) (2024)
- [Learning to Adapt: In-Context Learning Beyond Stationarity](https://mlsanity.com/paper/2604.10946/) (2026)
- [Sequence-Model-Guided Measurement Selection for Quantum State Learning](https://mlsanity.com/paper/2507.09891/) (2025)
- [Scalable bayesian shadow tomography for quantum property estimation with set transformers](https://mlsanity.com/paper/2509.18674/) (2025)
- [Noise-Robust Quantum State Characterization for Remote State Preparation with Deep Learning](https://mlsanity.com/paper/2609.20523/) (2026)
- [Generalization of Transformer-Based Neural Quantum States via In-Context Learning](https://mlsanity.com/paper/2610.03463/) (2026)

## Abstract (arXiv)

Quantum state tomography (QST) is the process of reconstructing the state of a quantum system (mathematically described as a density matrix) through a series of different measurements, which can be solved by learning a parameterized function to translate experimentally measured statistics into physical density matrices. However, the specific structure of quantum measurements for characterizing a quantum state has been neglected in previous work. In this paper, we explore the similarity between highly structured sentences in natural language and intrinsically structured measurements in QST. To fully leverage the intrinsic quantum characteristics involved in QST, we design a quantum-aware transformer (QAT) model to capture the complex relationship between measured frequencies and density matrices. In particular, we query quantum operators in the architecture to facilitate informative representations of quantum data and integrate the Bures distance into the loss function to evaluate quantum state fidelity, thereby enabling the reconstruction of quantum states from measured data with high fidelity. Extensive simulations and experiments (on IBM quantum computers) demonstrate the superiority of the QAT in reconstructing quantum states with favorable robustness against experimental noise.