# ShadowNet for Data-Centric Quantum System Learning

arXiv: https://arxiv.org/abs/2308.11290 · HTML: https://mlsanity.com/paper/2308.11290/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 107 references that are in the map.
- First posted on arXiv 22 Aug 2023.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Spatial Pyramid Pooling in Deep Convolutional Networks for Visual Recognition](https://mlsanity.com/paper/1406.4729/) (2014)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Understanding and Improving Layer Normalization](https://mlsanity.com/paper/1911.07013/) (2019)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [DataPerf: Benchmarks for Data-Centric AI Development](https://mlsanity.com/paper/2207.10062/) (2022)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [Efficient quantum tomography II](https://mlsanity.com/paper/1612.00034/) (2016)
- [Quantum State Tomography with Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2008.03240/) (2020)
- [Recent Advances for Quantum Neural Networks in Generative Learning](https://mlsanity.com/paper/2206.03066/) (2022)
- [Online Learning of Quantum States](https://mlsanity.com/paper/1802.09025/) (2018)
- [Recent advances for quantum classifiers](https://mlsanity.com/paper/2108.13421/) (2021)
- [Attention-based Quantum Tomography](https://mlsanity.com/paper/2006.12469/) (2020)
- [Learning many-body Hamiltonians with Heisenberg-limited scaling](https://mlsanity.com/paper/2210.03030/) (2022)
- [Enabling Multi-programming Mechanism for Quantum Computing in the NISQ Era](https://mlsanity.com/paper/2102.05321/) (2021)
- [Efficient estimation of Pauli observables by derandomization](https://mlsanity.com/paper/2103.07510/) (2021)
- [Problem-Dependent Power of Quantum Neural Networks on Multi-Class Classification](https://mlsanity.com/paper/2301.01597/) (2022)
- [Flexible learning of quantum states with generative query neural networks](https://mlsanity.com/paper/2202.06804/) (2022)
- [Adaptive Quantum State Tomography with Neural Networks](https://mlsanity.com/paper/1812.06693/) (2018)
- [Neural Error Mitigation of Near-Term Quantum Simulations](https://mlsanity.com/paper/2105.08086/) (2021)
- [Adaptive Online Learning of Quantum States](https://mlsanity.com/paper/2206.00220/) (2022)
- [Efficient Quantum State Sample Tomography with Basis-dependent Neural-networks](https://mlsanity.com/paper/2009.07601/) (2020)
- [Quantum Similarity Testing with Convolutional Neural Networks](https://mlsanity.com/paper/2211.01668/) (2022)
- [Deep learning of quantum entanglement from incomplete measurements](https://mlsanity.com/paper/2205.01462/) (2022)
- [Predicting Properties of Quantum Systems with Conditional Generative Models](https://mlsanity.com/paper/2211.16943/) (2022)

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

- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Multimodal deep representation learning for quantum cross-platform verification](https://mlsanity.com/paper/2311.03713/) (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)
- [Provably scalable learning from quantum many-body data via locality](https://mlsanity.com/paper/2509.13705/) (2025)
- [Learning from imperfect quantum data via unsupervised domain adaptation with classical shadows](https://mlsanity.com/paper/2603.28294/) (2026)

## Abstract (arXiv)

Understanding the dynamics of large quantum systems is hindered by the curse of dimensionality. Statistical learning offers new possibilities in this regime through neural network protocols and classical shadows, while both methods have limitations: the former suffers from incompatible dataset construction rules, resulting in substantial computational demands for data collection when addressing different tasks; the latter lacks the ability to distill knowledge from prior data to enhance subsequent learning endeavors. In this study, we propose a data-centric learning paradigm combining the strengths of these two approaches to advance quantum system learning (QSL). Central to our paradigm lies a unified dataset construction rule, achieved by classical shadows along with other easily obtainable information of quantum systems. To illustrate our approach, we present ShadowNet, implemented under both convolutional and attention mechanisms, to efficiently and faithfully tackle two pivotal QSL tasks: quantum state tomography (QST) and direct fidelity estimation (DFE). Numerical simulations on QST and DFE up to 60 qubits validate the efficacy of our proposal, showcasing how ShadowNet advances classical shadows with limited state copies, and highlighting how the varied neural networks impact the performance. Our work underscores the immense potential of a data-centric approach in comprehending novel and large quantum systems.