# Predicting Properties of Quantum Systems with Conditional Generative Models

arXiv: https://arxiv.org/abs/2211.16943 · HTML: https://mlsanity.com/paper/2211.16943/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 68 references that are in the map.
- First posted on arXiv 30 Nov 2022.

## Builds on (most cited first, 22 of 22)

- [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)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [Random Feature Attention](https://mlsanity.com/paper/2103.02143/) (2021)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [What Makes Convolutional Models Great on Long Sequence Modeling?](https://mlsanity.com/paper/2210.09298/) (2022)
- [Neural Kernels Without Tangents](https://mlsanity.com/paper/2003.02237/) (2020)
- [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)
- [Efficient estimation of Pauli observables by derandomization](https://mlsanity.com/paper/2103.07510/) (2021)
- [Learning hard quantum distributions with variational autoencoders](https://mlsanity.com/paper/1710.00725/) (2017)
- [Machine learning discovery of new phases in programmable quantum simulator snapshots](https://mlsanity.com/paper/2112.10789/) (2021)
- [Spacetime Neural Network for High Dimensional Quantum Dynamics](https://mlsanity.com/paper/2108.02200/) (2021)

## Built on by (most cited first, 9 of 9)

- [Improved machine learning algorithm for predicting ground state properties](https://mlsanity.com/paper/2301.13169/) (2023)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [ShadowNet for Data-Centric Quantum System Learning](https://mlsanity.com/paper/2308.11290/) (2023)
- [Predicting Ground State Properties: Constant Sample Complexity and Deep Learning Algorithms](https://mlsanity.com/paper/2405.18489/) (2024)
- [Rethink the Role of Deep Learning towards Large-scale Quantum Systems](https://mlsanity.com/paper/2505.13852/) (2025)
- [Photonic Quantum Computers](https://mlsanity.com/paper/2409.08229/) (2024)
- [Sequence-Model-Guided Measurement Selection for Quantum State Learning](https://mlsanity.com/paper/2507.09891/) (2025)
- [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)

Machine learning has emerged recently as a powerful tool for predicting properties of quantum many-body systems. For many ground states of gapped Hamiltonians, generative models can learn from measurements of a single quantum state to reconstruct the state accurately enough to predict local observables. Alternatively, classification and regression models can predict local observables by learning from measurements on different but related states. In this work, we combine the benefits of both approaches and propose the use of conditional generative models to simultaneously represent a family of states, learning shared structures of different quantum states from measurements. The trained model enables us to predict arbitrary local properties of ground states, even for states not included in the training data, without necessitating further training for new observables. We first numerically validate our approach on 2D random Heisenberg models using simulations of up to 45 qubits. Furthermore, we conduct quantum simulations on a neutral-atom quantum computer and demonstrate that our method can accurately predict the quantum phases of square lattices of 13×13 Rydberg atoms.