Machine learning (ML) algorithms have now become crucial in the field of High Energy Physics (HEP). An area where the application of such algorithms has proven particularly beneficial is the classification of hadronic jets produced at the Large Hadron Collider (LHC). Considering the complexity of the tasks in this field and the impending Run 3 data at higher luminosity, it is evident that a step-up in computational power is imperative. One potential candidate comes from the intersection between Quantum Computing (QC) and ML. Quantum Machine Learning (QML) algorithms leverage the intrinsic properties of QC, such as superposition and entanglement, to achieve better performance compared to their classical counterparts. This work provides an overview of these new learning models, with a focus in HEP. Specifically, we present studies of QML applications for the

 classification of jets produced (b vs. ¯ b and b vs. c)attheLHCbexperiment. Notably, we discuss recent developments in measuring entanglement entropy between

 qubits to gain new insights from the jet events data

Gianelle, A.

Lucchesi, D.

Monaco, S.

Nicotra, D

Sestini, L.

Zuliani, D.

Machine learning (ML) algorithms have now become crucial in the field of High Energy Physics (HEP). An area where the application of such algorithms has proven particularly beneficial is the classification of hadronic jets produced at the Large Hadron Collider (LHC). Considering the complexity of the tasks in this field and the impending Run 3 data at higher luminosity, it is evident that a step-up in computational power is imperative. One potential candidate comes from the intersection between Quantum Computing (QC) and ML. Quantum Machine Learning (QML) algorithms leverage the intrinsic properties of QC, such as superposition and entanglement, to achieve better performance compared to their classical counterparts. This work provides an overview of these new learning models, with a focus in HEP. Specifically, we present studies of QML applications for the classification of jets produced (b vs. b̄ and b vs. c) at the LHCb experiment. Notably, we discuss recent developments in measuring entanglement entropy between qubits to gain new insights from the jet events data.</p

Nicotra, D.

Maastricht University Research Portal

Quantum Machine Learning for data analysis at LHCb

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2024-24127-7Colloquia: IFAE 2023IL NUOVO CIMENTO 47 C (2024) 127Quantum Machine Learning for data analysis at LHCb(∗)A. Gianelle(1), D. Lucchesi(1)(2), S. Monaco(2), D. Nicotra(3)(4),L. Sestini(1)(2) and D. Zuliani(1)(2)(1) INFN, Sezione di Padova - Padova, Italy(2) Dipartimento di Fisica, Università di Padova - Padova, Italy(3) Nikhef National Institute for Subatomic Physics - Amsterdam, The Netherlands(4) University of Maastricht - Maastricht, The Netherlandsreceived 13 February 2024Summary. — Machine learning (ML) algorithms have now become crucial in thefield of High Energy Physics (HEP). An area where the application of such algo-rithms has proven particularly beneficial is the classification of hadronic jets pro-duced at the Large Hadron Collider (LHC). Considering the complexity of the tasksin this field and the impending Run 3 data at higher luminosity, it is evident thata step-up in computational power is imperative. One potential candidate comesfrom the intersection between Quantum Computing (QC) and ML. Quantum Ma-chine Learning (QML) algorithms leverage the intrinsic properties of QC, such assuperposition and entanglement, to achieve better performance compared to theirclassical counterparts. This work provides an overview of these new learning models,with a focus in HEP. Specifically, we present studies of QML applications for theclassification of jets produced (b vs. b̄ and b vs. c) at the LHCb experiment. No-tably, we discuss recent developments in measuring entanglement entropy betweenqubits to gain new insights from the jet events data.1. – Heavy Jets at LHCbJets are narrow cones of particles resulting from the strong interactions betweenquarks in proton-proton collisions. These collisions, occurring at high energies, initi-ate a cascade of processes leading to the formation of collimated streams of particles.The LHCb experiment stands out as a fitting tool for the study of jet formation,particularly those originating from heavy quarks. The unique geometry of LHCb in theforward region provides an advantageous and unique point of view for capturing eventswhere heavy quark jets are relevant.(∗) IFAE 2023 - “Poster” sessionCreative Commons Attribution 4.0 License (https://creativecommons.org/licenses/by/4.0) 12 A. GIANELLE et al.Machine learning (ML) applications currently leverage the intricate structure andcorrelations among all reconstructed particles to accurately identify the flavor of theoriginating quark. These ’black box’ implementations provide an ideal platform forthis task, as finding an analytical algorithm that encompasses all detected particles isimpossible.The complexity of this task, prompts the introduction of a new computing frameworkin order to achieve a better performance. Quantum Machine Learning (QML) modelsemerge as a promising candidate. Given the intricate nature of jet formation and thewealth of information embedded in each collision event, quantum models can amplify theefficiency and precision of jet classification.2. – Quantum Computing for Jets flavour identificationQuantum computers possess the capability to accurately evolve a quantum systemcomprising multiple quantum bits (qubits), gaining a computational advantage by har-nessing quantum mechanical phenomena, including entanglement.Operationally, we gain the ability to manipulate the wavefunction of the quantumsystem —a vector in the Hilbert space. Unlike a classical computer, which may be ableto simulate the evolution of such a system up to ∼ 20 qubits, an actual quantum imple-mentation allows us to scale up to the order of hundreds and even thousands of qubits.This scalability enables us to explore a significantly larger solution space, providing thepotential to capture more intricate relationships within the embedded input information.QML derives its fundamental concepts from classical ML. For instance, a gradient-based technique is employed to adjust the parameters of the operators responsible forevolving the wavefunction. This procedure aims to reach a minimum of a loss functiongiven by the specific task.3. – Jets classificationIn this section, we present the primary findings from two studies about jet taggingconducted by the LHCb Collaboration [1, 2].3.1. b vs. b̄ jet tagging . – The first study delved into the development of quantumtechniques for b vs. b̄ jets classifications. It is notoriously a difficult task, and currentmodels’ efficiencies are affected by a high value of rejection rate.Figure 1 shows a comparison in terms of tagging power εtag between two differentquantum models: “Angle Emb.” and “Amplitude Emb.”, as well as two classical meth-ods: “Muon Tag” and Deep Neural Network (DNN).3.2. b vs. c jet tagging . – b vs. c classification is a relatively easier ask, in which modelscan better exploit the jet’s substructure using the Secondary Vertex (SV) representationof the event. Figure 2 shows the bar-plots of the predictions of b-jets (marked in blue)and c-jets (marked in red) for the state-of-the-art classical architecture and a quantummodel.In both studies, the quantum methods showed slightly lower performances than theirclassical counterparts. It is crucial, however, to take into account that these novel meth-ods are still in the early stages of development and face constraints in terms of systemsize (number of qubits). Once both software and hardware implementations are furtherdeveloped, we expect to see the quantum models to show an advantage.QUANTUM MACHINE LEARNING FOR DATA ANALYSIS AT LHCb 3Fig. 1. – b vs. b̄ jet tagging - εtag with respect to (left) jet pT and (right) jet η [1].4. – Entanglement formation in a Quantum CircuitAn exclusive feature of quantum computation is the concept of generated entangle-ment. Throughout the training process, qubits exhibit varying degrees of entanglementamong each other. In the context of QML, entanglement plays a crucial role in fosteringcooperative behaviors between qubits, enabling the model to capture intricate patterns.Earlier studies have delved into the analysis of entanglement formation during thetraining process [3, 4]. The examination of this quantity is significant, as it has beendemonstrated to be correlated with the quality of the training process itself [5].Additionally, the phenomenon of entanglement formation opens opportunities for thedevelopment of various models aimed at gaining insights into the input dataset. Asan example, we present the results of a novel quantum model capable of getting theimportance and correlations among the features of the input data set.In fig. 3, a comparison is presented between the feature importances of 6 features fromthe SV dataset. These importances are computed using a classical model (PermutationImportance) and from the values of entanglement within the dedicated quantum model.Conversely, fig. 4 displays the correlation results of features from the SV dataset.The correlations have been computed using the quantum method (left), and with two“classical” metrics, namely the normalized mutual information (middle) and the Pearsonsquared coefficient (right).Fig. 2. – b vs. c jet tagging - predictions of the classical (left) and quantum model (right) [2].4 A. GIANELLE et al.Fig. 3. – Feature importance of 6 features of the SV data set computed with the Quantummethod and classical method [5].Features:1: vtx mCor2: vtx ipChi2Sum3: vtx nTrk4: vtx nTrkJet5: vtx ptSvrJet6: vtx ptFig. 4. – Correlation of the features using the fully quantum method (left), classical mutualinformation (middle), and the Pearson coefficient (right) [5].Since quantum methods exhibit greater expressiveness, entanglement-based modelsare potential candidates for revealing new hidden structures within the input data. Theabove results show similarities with their classical counterparts. However, further inves-tigation is required to determine whether their differences might reveal new informationabout the jet formation phenomena.REFERENCES[1] Gianelle Alessio et al., Quantum Machine Learning for b-jet charge identification,arXiv:2202.13943 (2022).[2] Cocha Carlos et al., Study of b-and c-jets identification with quantum machinelearning algorithms and application to the Higgs reconstruction, Master’s Thesis (2022)https://hdl.handle.net/20.500.12608/32223.[3] Ballarin Marco et al., Entanglement entropy production in Quantum Neural Networks,arXiv:2206.02474 (2022).[4] Felser Timo et al., npj Quantum Inf., 7 (2021) 111.[5] Monaco Saverio et al., Study of quantum correlations in LHCb simulated heavy flavourjets, Master’s Thesis (2022) https://hdl.handle.net/20.500.12608/51029.

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Quantum Machine Learning for data analysis at LHCb

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