# Classification and reconstruction of optical quantum states with deep neural networks

arXiv: https://arxiv.org/abs/2012.02185 · HTML: https://mlsanity.com/paper/2012.02185/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2020.

## Built on by (most cited first, 17 of 17)

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- [Quantum Conformal Prediction for Reliable Uncertainty Quantification in Quantum Machine Learning](https://mlsanity.com/paper/2304.03398/) (2023)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Exponentially improved efficient machine learning for quantum many-body states with provable guarantees](https://mlsanity.com/paper/2304.04353/) (2023)
- [Gradient-descent quantum process tomography by learning Kraus operators](https://mlsanity.com/paper/2208.00812/) (2022)
- [Fast quantum state reconstruction via accelerated non-convex programming](https://mlsanity.com/paper/2104.07006/) (2021)
- [Estimating the Euclidean quantum propagator with deep generative modeling of Feynman paths](https://mlsanity.com/paper/2202.02750/) (2022)
- [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)
- [Dimension-adaptive machine-learning-based quantum state reconstruction](https://mlsanity.com/paper/2205.05804/) (2022)
- [Improving application performance with biased distributions of quantum states](https://mlsanity.com/paper/2107.07642/) (2021)
- [Deep learning-based variational autoencoder for classification of quantum and classical states of light](https://mlsanity.com/paper/2405.05243/) (2024)
- [Reinforcement learning to learn quantum states for Heisenberg scaling accuracy](https://mlsanity.com/paper/2412.02334/) (2024)
- [A Distributed Hybrid Quantum Convolutional Neural Network for Medical Image Classification](https://mlsanity.com/paper/2501.06225/) (2025)
- [Tomography of time-dependent quantum spin networks with machine learning](https://mlsanity.com/paper/2103.08645/) (2021)
- [Quantum Down Sampling Filter for Variational Auto-encoder](https://mlsanity.com/paper/2501.06259/) (2025)
- [A Quantum Bagging Algorithm with Unsupervised Base Learners for Label Corrupted Datasets](https://mlsanity.com/paper/2509.07040/) (2025)

## Abstract (arXiv)

We apply deep-neural-network-based techniques to quantum state classification and reconstruction. We demonstrate high classification accuracies and reconstruction fidelities, even in the presence of noise and with little data. Using optical quantum states as examples, we first demonstrate how convolutional neural networks (CNNs) can successfully classify several types of states distorted by, e.g., additive Gaussian noise or photon loss. We further show that a CNN trained on noisy inputs can learn to identify the most important regions in the data, which potentially can reduce the cost of tomography by guiding adaptive data collection. Secondly, we demonstrate reconstruction of quantum-state density matrices using neural networks that incorporate quantum-physics knowledge. The knowledge is implemented as custom neural-network layers that convert outputs from standard feedforward neural networks to valid descriptions of quantum states. Any standard feed-forward neural-network architecture can be adapted for quantum state tomography (QST) with our method. We present further demonstrations of our proposed [arXiv:2008.03240] QST technique with conditional generative adversarial networks (QST-CGAN). We motivate our choice of a learnable loss function within an adversarial framework by demonstrating that the QST-CGAN outperforms, across a range of scenarios, generative networks trained with standard loss functions. For pure states with additive or convolutional Gaussian noise, the QST-CGAN is able to adapt to the noise and reconstruct the underlying state. The QST-CGAN reconstructs states using up to two orders of magnitude fewer iterative steps than a standard iterative maximum likelihood (iMLE) method. Further, the QST-CGAN can reconstruct both pure and mixed states from two orders of magnitude fewer randomly chosen data points than iMLE.