# Generative Invertible Quantum Neural Networks

arXiv: https://arxiv.org/abs/2302.12906 · HTML: https://mlsanity.com/paper/2302.12906/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 78 references that are in the map.
- First posted on arXiv 24 Feb 2023.

## Builds on (most cited first, 29 of 29)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [Experimental Quantum Generative Adversarial Networks for Image Generation](https://mlsanity.com/paper/2010.06201/) (2020)
- [Anomaly Detection with Density Estimation](https://mlsanity.com/paper/2001.04990/) (2020)
- [On the Quantum versus Classical Learnability of Discrete Distributions](https://mlsanity.com/paper/2007.14451/) (2020)
- [Rectangular Flows for Manifold Learning](https://mlsanity.com/paper/2106.01413/) (2021)
- [Anomaly Detection With Conditional Variational Autoencoders](https://mlsanity.com/paper/2010.05531/) (2020)
- [Recent Advances for Quantum Neural Networks in Generative Learning](https://mlsanity.com/paper/2206.03066/) (2022)
- [Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines](https://mlsanity.com/paper/1712.04144/) (2017)
- [MadMiner: Machine learning-based inference for particle physics](https://mlsanity.com/paper/1907.10621/) (2019)
- [Autoencoders for unsupervised anomaly detection in high energy physics](https://mlsanity.com/paper/2104.09051/) (2021)
- [How to GAN away Detector Effects](https://mlsanity.com/paper/1912.00477/) (2019)
- [Generative Networks for Precision Enthusiasts](https://mlsanity.com/paper/2110.13632/) (2021)
- [Quantum anomaly detection in the latent space of proton collision events at the LHC](https://mlsanity.com/paper/2301.10780/) (2023)
- [Style-based quantum generative adversarial networks for Monte Carlo events](https://mlsanity.com/paper/2110.06933/) (2021)
- [The Expressive Power of Parameterized Quantum Circuits](https://mlsanity.com/paper/1810.11922/) (2018)
- [Higgs analysis with quantum classifiers](https://mlsanity.com/paper/2104.07692/) (2021)
- [A Survey of Quantum Learning Theory](https://mlsanity.com/paper/1701.06806/) (2017)
- [Unravelling physics beyond the standard model with classical and quantum anomaly detection](https://mlsanity.com/paper/2301.10787/) (2023)
- [Information Scrambling in Quantum Neural Networks](https://mlsanity.com/paper/1909.11887/) (2019)
- [Learnability of the output distributions of local quantum circuits](https://mlsanity.com/paper/2110.05517/) (2021)
- [Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data](https://mlsanity.com/paper/2202.10471/) (2022)
- [Quantum-probabilistic Hamiltonian learning for generative modelling & anomaly detection](https://mlsanity.com/paper/2211.03803/) (2022)
- [Power of Quantum Generative Learning](https://mlsanity.com/paper/2205.04730/) (2022)
- [Invertible Manifold Learning for Dimension Reduction](https://mlsanity.com/paper/2010.04012/) (2020)

## Built on by (most cited first, 3 of 3)

- [Deep Generative Models for Detector Signature Simulation: A Taxonomic Review](https://mlsanity.com/paper/2312.09597/) (2023)
- [Jet Discrimination with Quantum Complete Graph Neural Network](https://mlsanity.com/paper/2403.04990/) (2024)
- [A multicategory jet image classification framework using deep neural network](https://mlsanity.com/paper/2407.03524/) (2024)

## Abstract (arXiv)

Invertible Neural Networks (INN) have become established tools for the simulation and generation of highly complex data. We propose a quantum-gate algorithm for a Quantum Invertible Neural Network (QINN) and apply it to the LHC data of jet-associated production of a Z-boson that decays into leptons, a standard candle process for particle collider precision measurements. We compare the QINN's performance for different loss functions and training scenarios. For this task, we find that a hybrid QINN matches the performance of a significantly larger purely classical INN in learning and generating complex data.