# On exploring the potential of quantum auto-encoder for learning quantum systems

arXiv: https://arxiv.org/abs/2106.15432 · HTML: https://mlsanity.com/paper/2106.15432/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 104 references that are in the map.
- First posted on arXiv 29 Jun 2021.

## Builds on (most cited first, 21 of 21)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Deep Learning for Spatio-Temporal Data Mining: A Survey](https://mlsanity.com/paper/1906.04928/) (2019)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Experimental Quantum Generative Adversarial Networks for Image Generation](https://mlsanity.com/paper/2010.06201/) (2020)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [Training Quantum Embedding Kernels on Near-Term Quantum Computers](https://mlsanity.com/paper/2105.02276/) (2021)
- [Towards understanding the power of quantum kernels in the NISQ era](https://mlsanity.com/paper/2103.16774/) (2021)
- [The dilemma of quantum neural networks](https://mlsanity.com/paper/2106.04975/) (2021)
- [Quantum autoencoders via quantum adders with genetic algorithms](https://mlsanity.com/paper/1709.07409/) (2017)
- [Experimental Implementation of a Quantum Autoencoder via Quantum Adders](https://mlsanity.com/paper/1807.10643/) (2018)
- [Variational Quantum Algorithms for Trace Distance and Fidelity Estimation](https://mlsanity.com/paper/2012.05768/) (2020)
- [Variational quantum Gibbs state preparation with a truncated Taylor series](https://mlsanity.com/paper/2005.08797/) (2020)
- [Experimental measurement of Hilbert-Schmidt distance between two-qubit states as means for speeding-up machine learning](https://mlsanity.com/paper/1907.02292/) (2019)

## Built on by (most cited first, 6 of 6)

- [Recent Advances for Quantum Neural Networks in Generative Learning](https://mlsanity.com/paper/2206.03066/) (2022)
- [Problem-Dependent Power of Quantum Neural Networks on Multi-Class Classification](https://mlsanity.com/paper/2301.01597/) (2022)
- [Power of Quantum Generative Learning](https://mlsanity.com/paper/2205.04730/) (2022)
- [Transition Role of Entangled Data in Quantum Machine Learning](https://mlsanity.com/paper/2306.03481/) (2023)
- [Neural Architecture Search for Quantum Autoencoders](https://mlsanity.com/paper/2511.19246/) (2025)
- [QiNN-QJ: A Quantum-inspired Neural Network with Quantum Jump for Multimodal Sentiment Analysis](https://mlsanity.com/paper/2510.27091/) (2025)

## Abstract (arXiv)

The frequent interactions between quantum computing and machine learning revolutionize both fields. One prototypical achievement is the quantum auto-encoder (QAE), as the leading strategy to relieve the curse of dimensionality ubiquitous in the quantum world. Despite its attractive capabilities, practical applications of QAE have yet largely unexplored. To narrow this knowledge gap, here we devise three effective QAE-based learning protocols to address three classically computational hard learning problems when learning quantum systems, which are low-rank state fidelity estimation, quantum Fisher information estimation, and Gibbs state preparation. Attributed to the versatility of QAE, our proposals can be readily executed on near-term quantum machines. Besides, we analyze the error bounds of the trained protocols and showcase the necessary conditions to provide practical utility from the perspective of complexity theory. We conduct numerical simulations to confirm the effectiveness of the proposed three protocols. Our work sheds new light on developing advanced quantum learning algorithms to accomplish hard quantum physics and quantum information processing tasks.