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arXiv:2101.05618

A Digital Quantum Algorithm for Jet Clustering in High-Energy Physics

Pires, Diogo, P. Bargassa, J. Seixas, Yasser Omar

Published Jan 11, 2021• 9 citations
arXivHTMLPDF

Abstract

Experimental High-Energy Physics (HEP), especially the Large Hadron Collider (LHC) programme at the European Organization for Nuclear Research (CERN), is one of the most computationally intensive activities in the world. This demand is set to increase significantly with the upcoming High-Luminosity LHC (HL-LHC), and even more in future machines, such as the Future Circular Collider (FCC). As a consequence, event reconstruction, and in particular jet clustering, is bound to become an even more daunting problem, thus challenging present day computing resources. In this work, we present the first digital quantum algorithm to tackle jet clustering, opening the way for digital quantum processors to address this challenging problem. Furthermore, we show that, at present and future collider energies, our algorithm has comparable, yet generally lower complexity relative to the classical state-of-the-art $k_t$ clustering algorithm.

DOI
10.48550/arxiv.2101.05618

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Experimental High-Energy Physics (HEP), especially the Large Hadron Collider (LHC) programme at the European Organization for Nuclear Research (CERN), is one of the most computationally intensive activities in the world. This demand is set to increase significantly with the upcoming High-Luminosity LHC (HL-LHC), and even more in future machines, such as the Future Circular Collider (FCC). As a consequence, event reconstruction, and in particular jet clustering, is bound to become an even more daunting problem, thus challenging present day computing resources. In this work, we present the first digital quantum algorithm to tackle jet clustering, opening the way for digital quantum processors to address this challenging problem. Furthermore, we show that, at present and future collider energies, our algorithm has comparable, yet generally lower complexity relative to the classical state-of-the-art ktk_tkt​ clustering algorithm.
The currently predicted increase in computational demand for the upcoming High-Luminosity Large Hadron Collider (HL-LHC) event reconstruction, and in particular jet clustering, is bound to challenge present day computing resources, becoming an even more complex combinatorial problem. In this paper, we show that quantum annealing can tackle dijet event clustering by introducing a novel quantum annealing binary clustering algorithm. The benchmarked efficiency is of the order of 96%, thus yielding substantial improvements over the current quantum state-of-the-art. Additionally, we also show how to generalize the proposed objective function into a more versatile form, capable of solving the clustering problem in multijet events.
Clustering is one of the most frequent problems in many domains, in particular, in particle physics where jet reconstruction is central in experimental analyses. Jet clustering at the CERN's Large Hadron Collider (LHC) is computationally expensive and the difficulty of this task will increase with the upcoming High-Luminosity LHC (HL-LHC). In this paper, we study the case in which quantum computing algorithms might improve jet clustering by considering two novel quantum algorithms which may speed up the classical jet clustering algorithms. The first one is a quantum subroutine to compute a Minkowski-based distance between two data points, whereas the second one consists of a quantum circuit to track the maximum into a list of unsorted data. The latter algorithm could be of value beyond particle physics, for instance in statistics. When one or both of these algorithms are implemented into the classical versions of well-known clustering algorithms (K-means, affinity propagation, and kT{k}_{T}kT​-jet) we obtain efficiencies comparable to those of their classical counterparts. Even more, exponential speed-up could be achieved, in the first two algorithms, in data dimensionality and data length when the distance algorithm or the maximum searching algorithm are applied.
Identifying jets formed in high-energy particle collisions requires solving optimization problems over potentially large numbers of final-state particles. In this work, we consider the possibility of using quantum computers to speed up jet clustering algorithms. Focusing on the case of electron-positron collisions, we consider a well-known event shape called thrust whose optimum corresponds to the most jetlike separating plane among a set of particles, thereby defining two hemisphere jets. We show how to formulate thrust both as a quantum annealing problem and as a Grover search problem. A key component of our analysis is the consideration of realistic models for interfacing classical data with a quantum algorithm. With a sequential computing model, we show how to speed up the well-known O(N3)O({N}^{3})O(N3) classical algorithm to an O(N2)O({N}^{2})O(N2) quantum algorithm, including the O(N)O(N)O(N) overhead of loading classical data from NNN final-state particles. Along the way, we also identify a way to speed up the classical algorithm to O(N2logN)O({N}^{2}\mathrm{log}N)O(N2logN) using a sorting strategy inspired by the siscone jet algorithm, which has no natural quantum counterpart. With a parallel computing model, we achieve O(NlogN)O(N\mathrm{log}N)O(NlogN) scaling in both the classical and quantum cases. Finally, we consider the generalization of these quantum methods to other jet algorithms more closely related to those used for proton-proton collisions at the Large Hadron Collider.
High-energy physics is facing a daunting computing challenge with the large amount of data expected from the HL-LHC and other future colliders. In addition, the landscape of computation has been expanding dramatically with technologies beyond the standard x86 CPU architecture becoming increasingly available. Both of these factors necessitate an extensive and broad-ranging research and development campaign. As quantum computation has been evolving rapidly over the past few years, it is important to evaluate how quantum computation could be one potential avenue for development for future collider experiments. A wide variety of applications have been considered by different authors. We review here selected applications of quantum computing to high-energy physics, including topics in simulation, reconstruction, and the use of machine learning, and their challenges. In addition, recent advances in quantum computing technology to enhance such applications are briefly highlighted. Finally, we will discuss how such applications might transform the workflows of future collider experiments and highlight other potential applications.
High-energy physics is facing a daunting computing challenge with the large datasets expected from the upcoming High-Luminosity Large Hadron Collider in the next decade and even more so at future colliders. A key challenge in the reconstruction of events of simulated data and collision data is the pattern recognition algorithms used to determine the trajectories of charged particles. The field of quantum computing shows promise for transformative capabilities and is going through a cycle of rapid development and hence might provide a solution to this challenge. This article reviews current studies of quantum computers for charged particle pattern recognition in high-energy physics. This article is part of the theme issue 'Quantum technologies in particle physics'.
Machine Learning algorithms are playing a fundamental role in solving High Energy Physics tasks. In particular, the classification of hadronic jets at the Large Hadron Collider is suited for such types of algorithms, and despite the great effort that has been put in place to tackle such a classification task, there is room for improvement. In this context, Quantum Machine Learning is a new methodology that takes advantage of the intrinsic properties of quantum computation (e.g. entanglement between qubits) to possibly improve the performance of a classification task. In this contribution, a new study of Quantum Machine Learning applied to jet identification is presented. Namely, a Variational Quantum Classifier is trained and evaluated on fully simulated data of the LHCb experiment, in order to identify jets containing a hadron formed by a bbb or bˉ\bar{b}bˉ quark at the moment of production. The jet identification performance of the quantum classifier is compared with a Deep Neural Network using the same input features.