# Quantum State Tomography with Conditional Generative Adversarial Networks

arXiv: https://arxiv.org/abs/2008.03240 · HTML: https://mlsanity.com/paper/2008.03240/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2020.

## Built on by (most cited first, 30 of 41)

- [Autoregressive neural-network wavefunctions for ab initio quantum chemistry](https://mlsanity.com/paper/2109.12606/) (2021)
- [Flexible learning of quantum states with generative query neural networks](https://mlsanity.com/paper/2202.06804/) (2022)
- [Learning quantum data with the quantum Earth Mover's distance](https://mlsanity.com/paper/2101.03037/) (2021)
- [Quantum Similarity Testing with Convolutional Neural Networks](https://mlsanity.com/paper/2211.01668/) (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)
- [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)
- [Exponentially improved efficient machine learning for quantum many-body states with provable guarantees](https://mlsanity.com/paper/2304.04353/) (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)
- [Power of Quantum Generative Learning](https://mlsanity.com/paper/2205.04730/) (2022)
- [Gradient-descent quantum process tomography by learning Kraus operators](https://mlsanity.com/paper/2208.00812/) (2022)
- [Quantum computing and artificial intelligence: status and perspectives](https://mlsanity.com/paper/2505.23860/) (2025)
- [Fast quantum state reconstruction via accelerated non-convex programming](https://mlsanity.com/paper/2104.07006/) (2021)
- [Rethink the Role of Deep Learning towards Large-scale Quantum Systems](https://mlsanity.com/paper/2505.13852/) (2025)
- [Estimating the Euclidean quantum propagator with deep generative modeling of Feynman paths](https://mlsanity.com/paper/2202.02750/) (2022)
- [Noise-Agnostic Quantum Error Mitigation with Data Augmented Neural Models](https://mlsanity.com/paper/2311.01727/) (2023)
- [Variational Quantum Circuits Enhanced Generative Adversarial Network](https://mlsanity.com/paper/2402.01791/) (2024)
- [Optical Quantum Mixed-State Reconstruction With Multiple Deep Learning Approaches](https://mlsanity.com/paper/2407.01734/) (2024)
- [Single-preparation unsupervised quantum machine learning: concepts and applications](https://mlsanity.com/paper/2101.01442/) (2021)
- [Generative Adversarial Network for Probabilistic Forecast of Random Dynamical System](https://mlsanity.com/paper/2111.03126/) (2021)
- [Dimension-adaptive machine-learning-based quantum state reconstruction](https://mlsanity.com/paper/2205.05804/) (2022)
- [Adversarial Data Poisoning Attacks on Quantum Machine Learning in the NISQ Era](https://mlsanity.com/paper/2411.14412/) (2024)
- [QGAN-based data augmentation for hybrid quantum-classical neural networks](https://mlsanity.com/paper/2505.24780/) (2025)
- [Two-dimensional total absorption spectroscopy with conditional generative adversarial networks](https://mlsanity.com/paper/2206.11792/) (2022)
- [Fast Minimization of Expected Logarithmic Loss via Stochastic Dual Averaging](https://mlsanity.com/paper/2311.02557/) (2023)
- [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)
- [Parametric Quantum State Tomography with HyperRBMs](https://mlsanity.com/paper/2601.20950/) (2026)

## Abstract (arXiv)

Quantum state tomography (QST) is a challenging task in intermediate-scale quantum devices. Here, we apply conditional generative adversarial networks (CGANs) to QST. In the CGAN framework, two duelling neural networks, a generator and a discriminator, learn multi-modal models from data. We augment a CGAN with custom neural-network layers that enable conversion of output from any standard neural network into a physical density matrix. To reconstruct the density matrix, the generator and discriminator networks train each other on data using standard gradient-based methods. We demonstrate that our QST-CGAN reconstructs optical quantum states with high fidelity orders of magnitude faster, and from less data, than a standard maximum-likelihood method. We also show that the QST-CGAN can reconstruct a quantum state in a single evaluation of the generator network if it has been pre-trained on similar quantum states.