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Generative quantum machine learning for particle physics

L. Sestini

Published Mar 5, 2026• 0 citations
Publisher

Abstract

In this notebook a quantum Generative Adversarial Network is trained for the simulation of a calorimeter module of the LHCb experiment. The calorimeter module measure energy deposits as images of 8x8 pixels. The discriminator is a classical neural network and the generator is a variational quantum circuit. Several figures of merit are studied to validate the simulation, as the Kolmogorov-Smirnov test for the distribution of total measured energy, and the RSME test compatibility of calorimeter images.

DOI
10.5281/zenodo.18877707

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In this notebook a quantum Generative Adversarial Network is trained for the simulation of a calorimeter module of the LHCb experiment. The calorimeter module measure energy deposits as images of 8x8 pixels. The discriminator is a classical neural network and the generator is a variational quantum circuit. Several figures of merit are studied to validate the simulation, as the Kolmogorov-Smirnov test for the distribution of total measured energy, and the RSME test compatibility of calorimeter images.
Abstract The prospect of quantum computing with a potential exponential speed-up compared to classical computing identifies it as a promising method in the search for alternative future High Energy Physics (HEP) simulation approaches. HEP simulations, such as employed at the Large Hadron Collider at CERN, are extraordinarily complex and require an immense amount of computing resources in hardware and time. For some HEP simulations, classical machine learning models have already been successfully developed and tested, resulting in several orders of magnitude speed-up. In this research, we proceed to the next step and explore whether quantum computing can provide sufficient accuracy, and further improvements, suggesting it as an exciting direction of future investigations. With a small prototype model, we demonstrate a full quantum Generative Adversarial Network (GAN) model for generating downsized eight-pixel calorimeter shower images. The advantage over previous quantum models is that the model generates real individual images containing pixel energy values instead of simple probability distributions averaged over a test sample. To complete the picture, the results of the full quantum GAN model are compared to hybrid quantum-classical models using a classical discriminator neural network.
Quantum Computing has emerged as a viable alternative to classical computing for a number of different tasks, with the idea of a potential speedup in mind. One of the most promising fields of research in quantum computing is Quantum Machine Learning. An interesting area of application for Quantum Machine Learning can be found in High Energy Physics: one key component of creating experiments in a particle accelerator like the Large Hadron Collider is the simulation of those experiments beforehand, in order to gain a better understanding of the results actually measured. Those types of simulations, typically based on Monte-Carlo methods, require significant computing resources and, as we approach CERN's High Luminosity Phase, there is a strong need for more efficient and cost controlled simulations. In this thesis a model based on Quantum Generative Adversarial Networks (QGANs) is implemented, with the intention of exploring potential quantum computing advantages within a hybrid machine learning model that is tasked with the generation of calorimeter samples. The model is initially trained on an ideal simulator to ensure that the results are comparable to those of a similar classical model. Finally, the model is modified in order to effectively run on a real quantum device and the training is executed in its entirety on a 54-qubit quantum processor.
Abstract A hybrid quantum–classical approach to model continuous classical probability distributions using a variational quantum circuit is proposed. The architecture of this quantum generator consists of a quantum circuit that encodes a classical random variable into a quantum state and a parameterized quantum circuit trained to mimic the target distribution. The model allows for easy interfacing with a classical function, such as a neural network, and is trained using an adversarial learning approach. It is shown that the quantum generator is able to learn using either a classical neural network or a variational quantum circuit as the discriminator model. This implementation takes advantage of automatic differentiation tools to perform the optimization of the variational circuits employed. The framework presented here for the design and implementation of the variational quantum generators can serve as a blueprint for designing hybrid quantum–classical models for other machine learning tasks.
Generative models, and Generative Adversarial Networks (GAN) in particular, are being studied as possible alternatives to Monte Carlo simulations. It has been proposed that, in certain circumstances, simulation using GANs can be sped-up by using quantum GANs (qGANs). We present a new design of qGAN, the dual-Parameterized Quantum Circuit (PQC) GAN, which consists of a classical discriminator and two quantum generators which take the form of PQCs. The first PQC learns a probability distribution over N-pixel images, while the second generates normalized pixel intensities of an individual image for each PQC input. With a view to HEP applications, we evaluated the dual-PQC architecture on the task of imitating calorimeter outputs, translated into pixelated images. The results demonstrate that the model can reproduce a fixed number of images with a reduced size as well as their probability distribution and we anticipate it should allow us to scale up to real calorimeter outputs.
Generative models, and Generative Adversarial Networks (GAN) in particular, are being studied as possible alternatives to Monte Carlo simulations. It has been proposed that, in certain circumstances, simulation using GANs can be sped-up by using quantum GANs (qGANs). We present a new design of qGAN, the dual-Parameterized Quantum Circuit (PQC) GAN, which consists of a classical discriminator and two quantum generators which take the form of PQCs. The first PQC learns a probability distribution over N-pixel images, while the second generates normalized pixel intensities of an individual image for each PQC input. With a view to HEP applications, we evaluated the dual-PQC architecture on the task of imitating calorimeter outputs, translated into pixelated images. The results demonstrate that the model can reproduce a fixed number of images with a reduced size as well as their probability distribution and we anticipate it should allow us to scale up to real calorimeter outputs.
The increasing demands on simulation statistics for HL-LHC analyses challenge the scalability of traditional calorimeter simulation within all LHC collaborations. Fast simulation techniques based on machine learning have proven effective, yet further improvement may arise from quantum-inspired models. In this study we investigate the feasibility of integrating Quantum Neural Network (QNN) components into the ATLAS fast calorimeter simulation framework, to evaluate potential gain in generative performance and generalisation. We focus on a hybrid pipeline where a quantum Generative Adversarial Network (qGAN) is employed, whose generator is composed of a Parametrised Quantum Circuit (PQC) followed by a classical neural network, while the discriminator is kept classical. We report on implementation details, benchmarking against established fast simulation components, and performance metrics. Preliminary results show that qGAN models are technically feasible within ATLAS software and are promising for benefit with respect to the classical ATLAS fast simulation system.