# Attention-based Quantum Tomography

arXiv: https://arxiv.org/abs/2006.12469 · HTML: https://mlsanity.com/paper/2006.12469/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2020.

## Built on by (most cited first, 26 of 26)

- [Quantum Vision Transformers](https://mlsanity.com/paper/2209.08167/) (2022)
- [Quantum Self-Attention Neural Networks for Text Classification](https://mlsanity.com/paper/2205.05625/) (2022)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Predicting Properties of Quantum Systems with Conditional Generative Models](https://mlsanity.com/paper/2211.16943/) (2022)
- [Multimodal deep representation learning for quantum cross-platform verification](https://mlsanity.com/paper/2311.03713/) (2023)
- [The autoregressive neural network architecture of the Boltzmann distribution of pairwise interacting spins systems](https://mlsanity.com/paper/2302.08347/) (2023)
- [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)
- [Quantum State Tomography using Quantum Machine Learning](https://mlsanity.com/paper/2308.10327/) (2023)
- [Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits](https://mlsanity.com/paper/2408.12199/) (2024)
- [Quantum computing and artificial intelligence: status and perspectives](https://mlsanity.com/paper/2505.23860/) (2025)
- [Hamiltonian-Driven Shadow Tomography of Quantum States](https://mlsanity.com/paper/2102.10132/) (2021)
- [Combining machine learning with physics: A framework for tracking and sorting multiple dark solitons](https://mlsanity.com/paper/2111.04881/) (2021)
- [Empirical Sample Complexity of Neural Network Mixed State Reconstruction](https://mlsanity.com/paper/2307.01840/) (2023)
- [Rethink the Role of Deep Learning towards Large-scale Quantum Systems](https://mlsanity.com/paper/2505.13852/) (2025)
- [Agentic Publication Protocol: An Attempt to Modernize Scientific Publication](https://mlsanity.com/paper/2606.27386/) (2026)
- [Learning quantum symmetries with interactive quantum-classical variational algorithms](https://mlsanity.com/paper/2206.11970/) (2022)
- [Reinforcement learning to learn quantum states for Heisenberg scaling accuracy](https://mlsanity.com/paper/2412.02334/) (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)
- [Autoregressive model path dependence near Ising criticality](https://mlsanity.com/paper/2408.15715/) (2024)
- [Entanglement Detection with Quantum-inspired Kernels and SVMs](https://mlsanity.com/paper/2508.17909/) (2025)
- [Vectorized Attention with Learnable Encoding for Quantum Transformer](https://mlsanity.com/paper/2508.18464/) (2025)
- [Fixed-Protocol Amortized MPS Tomography with Conformalized Predictive Uncertainty](https://mlsanity.com/paper/2607.11273/) (2026)
- [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)

With rapid progress across platforms for quantum systems, the problem of many-body quantum state reconstruction for noisy quantum states becomes an important challenge. Recent works found promise in recasting the problem of quantum state reconstruction to learning the probability distribution of quantum state measurement vectors using generative neural network models. Here we propose the "Attention-based Quantum Tomography" (AQT), a quantum state reconstruction using an attention mechanism-based generative network that learns the mixed state density matrix of a noisy quantum state. The AQT is based on the model proposed in "Attention is all you need" by Vishwani et al (2017) that is designed to learn long-range correlations in natural language sentences and thereby outperform previous natural language processing models. We demonstrate not only that AQT outperforms earlier neural-network-based quantum state reconstruction on identical tasks but that AQT can accurately reconstruct the density matrix associated with a noisy quantum state experimentally realized in an IBMQ quantum computer. We speculate the success of the AQT stems from its ability to model quantum entanglement across the entire quantum system much as the attention model for natural language processing captures the correlations among words in a sentence.