# Quantum Inception Score

arXiv: https://arxiv.org/abs/2311.12163 · HTML: https://mlsanity.com/paper/2311.12163/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 105 references that are in the map.
- First posted on arXiv 20 Nov 2023.

## Builds on (most cited first, 20 of 20)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Wild Patterns: Ten Years After the Rise of Adversarial Machine Learning](https://mlsanity.com/paper/1712.03141/) (2017)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [A Note on the Inception Score](https://mlsanity.com/paper/1801.01973/) (2018)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Quantum generative adversarial networks](https://mlsanity.com/paper/1804.08641/) (2018)
- [Absence of Barren Plateaus in Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2011.02966/) (2020)
- [Quantum machine learning beyond kernel methods](https://mlsanity.com/paper/2110.13162/) (2021)
- [Experimental Quantum Generative Adversarial Networks for Image Generation](https://mlsanity.com/paper/2010.06201/) (2020)
- [Quantum Variational Autoencoder](https://mlsanity.com/paper/1802.05779/) (2018)
- [Enhancing Generative Models via Quantum Correlations](https://mlsanity.com/paper/2101.08354/) (2021)
- [On barren plateaus and cost function locality in variational quantum algorithms](https://mlsanity.com/paper/2011.10530/) (2020)
- [Recent advances for quantum classifiers](https://mlsanity.com/paper/2108.13421/) (2021)
- [Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits](https://mlsanity.com/paper/2001.00550/) (2020)
- [On compression rate of quantum autoencoders: Control design, numerical and experimental realization](https://mlsanity.com/paper/2005.11149/) (2020)
- [Generalization Metrics for Practical Quantum Advantage in Generative Models](https://mlsanity.com/paper/2201.08770/) (2022)

## Built on by (most cited first, 2 of 2)

- [Learning to Classify Quantum Phases of Matter with a Few Measurements](https://mlsanity.com/paper/2409.05188/) (2024)
- [Learning Topological Quantum Phases from Limited Subsystems](https://mlsanity.com/paper/2607.10656/) (2026)

## Abstract (arXiv)

Motivated by the great success of classical generative models in machine learning, enthusiastic exploration of their quantum version has recently started. To depart on this journey, it is important to develop a relevant metric to evaluate the quality of quantum generative models; in the classical case, one such example is the (classical) inception score (cIS). In this paper, as a natural extension of cIS, we propose the quantum inception score (qIS) for quantum generators. Importantly, qIS relates the quality to the Holevo information of the quantum channel that classifies a given dataset. In this context, we show several properties of qIS. First, qIS is greater than or equal to the corresponding cIS, which is defined through projection measurements on the system output. Second, the difference between qIS and cIS arises from the presence of quantum coherence, as characterized by the resource theory of asymmetry. Third, when a set of entangled generators is prepared, there exists a classifying process leading to the further enhancement of qIS. Fourth, we harness the quantum fluctuation theorem to characterize the physical limitation of qIS. Finally, we apply qIS to assess the quality of the one-dimensional spin chain model as a quantum generative model, with the quantum convolutional neural network as a quantum classifier, for the phase classification problem in the quantum many-body physics.