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002764310 0247_ $$2DOI$$9APS$$a10.1103/PhysRevResearch.3.033221$$qpublication
002764310 037__ $$9arXiv$$aarXiv:2104.05059$$cquant-ph
002764310 037__ $$aFERMILAB-PUB-21-552-DI-QIS
002764310 035__ $$9arXiv$$aoai:arXiv.org:2104.05059
002764310 035__ $$9Inspire$$aoai:inspirehep.net:1857931$$d2023-12-06T13:38:45Z$$h2023-12-07T03:00:06Z$$mmarcxml$$ttrue$$uhttps://inspirehep.net/api/oai2d
002764310 035__ $$9Inspire$$a1857931
002764310 041__ $$aeng
002764310 100__ $$aWu, Sau Lan$$jORCID:[email protected]$$uWisconsin U., Madison$$vDepartment of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
002764310 245__ $$9APS$$aApplication of Quantum Machine Learning using the Quantum Kernel Algorithm on High Energy Physics Analysis at the LHC
002764310 269__ $$c2021-04-11
002764310 260__ $$c2021-09-08
002764310 300__ $$a9 p
002764310 520__ $$9APS$$aQuantum machine learning could possibly become a valuable alternative to classical machine learning for applications in high energy physics by offering computational speedups. In this study, we employ a support vector machine with a quantum kernel estimator (QSVM-Kernel method) to a recent LHC flagship physics analysis: <math><mrow><mi>t</mi><mover accent="true"><mi>t</mi><mo>¯</mo></mover><mi>H</mi></mrow></math> (Higgs boson production in association with a top quark pair). In our quantum simulation study using up to 20 qubits and up to <math><mrow><mn>50</mn><mspace width="0.16em"/><mn>000</mn></mrow></math> events, the QSVM-Kernel method performs as well as its classical counterparts in three different platforms from Google Tensorflow Quantum, IBM Quantum, and Amazon Braket. Additionally, using 15 qubits and 100 events, the application of the QSVM-Kernel method on the IBM superconducting quantum hardware approaches the performance of a noiseless quantum simulator. Our study confirms that the QSVM-Kernel method can use the large dimensionality of the quantum Hilbert space to replace the classical feature space in realistic physics data sets.
002764310 520__ $$9arXiv$$aQuantum machine learning could possibly become a valuable alternative to classical machine learning for applications in High Energy Physics by offering computational speed-ups. In this study, we employ a support vector machine with a quantum kernel estimator (QSVM-Kernel method) to a recent LHC flagship physics analysis: $t\bar{t}H$ (Higgs boson production in association with a top quark pair). In our quantum simulation study using up to 20 qubits and up to 50000 events, the QSVM-Kernel method performs as well as its classical counterparts in three different platforms from Google Tensorflow Quantum, IBM Quantum and Amazon Braket. Additionally, using 15 qubits and 100 events, the application of the QSVM-Kernel method on the IBM superconducting quantum hardware approaches the performance of a noiseless quantum simulator. Our study confirms that the QSVM-Kernel method can use the large dimensionality of the quantum Hilbert space to replace the classical feature space in realistic physics datasets.
002764310 540__ $$3preprint$$aarXiv nonexclusive-distrib 1.0$$uhttp://arxiv.org/licenses/nonexclusive-distrib/1.0/
002764310 540__ $$3publication$$aCC BY 4.0$$uhttps://creativecommons.org/licenses/by/4.0/
002764310 542__ $$3publication$$dauthors$$g2021
002764310 65017 $$2arXiv$$ahep-ex
002764310 65017 $$2SzGeCERN$$aParticle Physics - Experiment
002764310 65017 $$2arXiv$$aquant-ph
002764310 65017 $$2SzGeCERN$$aGeneral Theoretical Physics
002764310 690C_ $$aCERN
002764310 690C_ $$aARTICLE
002764310 700__ $$aSun, Shaojun$$uWisconsin U., Madison$$vDepartment of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
002764310 700__ $$aGuan, Wen$$jORCID:0000-0002-5548-5194$$uWisconsin U., Madison$$vDepartment of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
002764310 700__ $$aZhou, Chen$$uWisconsin U., Madison$$vDepartment of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
002764310 700__ $$aChan, Jay$$uWisconsin U., Madison$$vDepartment of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
002764310 700__ $$aCheng, Chi Lung$$uWisconsin U., Madison$$vDepartment of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
002764310 700__ $$aPham, Tuan$$uWisconsin U., Madison$$vDepartment of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
002764310 700__ $$aQian, Yan$$jORCID:0000-0002-9324-6354$$uWisconsin U., Madison$$vDepartment of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
002764310 700__ $$aWang, Alex Zeng$$uWisconsin U., Madison$$vDepartment of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
002764310 700__ $$aZhang, Rui$$jORCID:0000-0002-8265-474X$$uWisconsin U., Madison$$vDepartment of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
002764310 700__ $$aLivny, Miron$$jORCID:0000-0001-5444-7439$$uWisconsin U., Madison$$vDepartment of Computer Sciences, University of Wisconsin, Madison, Wisconsin 53706, USA
002764310 700__ $$aGlick, Jennifer$$uIBM Watson Res. Ctr.$$vIBM Quantum, T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
002764310 700__ $$aBarkoutsos, Panagiotis Kl.$$uIBM, Zurich$$vIBM Quantum, Zurich Research Laboratory, CH-8803 Rüschlikon, Switzerland
002764310 700__ $$aWoerner, Stefan$$uIBM, Zurich$$vIBM Quantum, Zurich Research Laboratory, CH-8803 Rüschlikon, Switzerland
002764310 700__ $$aTavernelli, Ivano$$uIBM, Zurich$$vIBM Quantum, Zurich Research Laboratory, CH-8803 Rüschlikon, Switzerland
002764310 700__ $$aCarminati, Federico$$uCERN$$vCERN Quantum Technology Initiative, IT Department, CERN, CH-1211 Geneva, Switzerland
002764310 700__ $$aDi Meglio, Alberto$$jORCID:0000-0001-6466-5413$$uCERN$$vCERN Quantum Technology Initiative, IT Department, CERN, CH-1211 Geneva, Switzerland
002764310 700__ $$aLi, Andy C.Y.$$jORCID:0000-0003-4542-3739$$uFermilab$$vQuantum Institute, Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
002764310 700__ $$aLykken, Joseph$$uFermilab$$vQuantum Institute, Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
002764310 700__ $$aSpentzouris, Panagiotis$$uFermilab$$vQuantum Institute, Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
002764310 700__ $$aChen, Samuel Yen-Chi$$jORCID:0000-0003-0114-4826$$uBrookhaven$$vComputational Science Initiative, Brookhaven National Laboratory, Upton, New York 11973, USA
002764310 700__ $$aYoo, Shinjae$$jORCID:0000-0003-4378-6448$$uBrookhaven$$vComputational Science Initiative, Brookhaven National Laboratory, Upton, New York 11973, USA
002764310 700__ $$aWei, Tzu-Chieh$$uYITP, Stony Brook$$vC.N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, New York 11794, USA
002764310 773__ $$c033221$$mpublication$$n3$$pPhys. Rev. Res.$$v3$$xPhys. Rev. Research 3, 033221 (2021)$$y2021
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002764310 8564_ $$82288806$$s40048$$uhttps://cds.cern.ch/record/2764310/files/fig7a.png$$y00012 AUCs of the QSVM-Kernel algorithm as a function of the number of qubits (10 to 20 qubits). The number of qubits is equal to the number of input variables. The 60 statistically independent \ttH\ analysis datasets of 20000 events are used in this study. In (a), we compare the results of the QSVM-Kernel classifier (on the \textit{qsim Simulator} from the Google TensorFlow Quantum framework) with the results of the classical SVM and classical BDT classifiers using the same input variables. In (b), we further display the difference between the QSVM-Kernel results and the classical machine learning results. In (c), we compare the \textit{qsim Simulator} from the Google TensorFlow Quantum framework, the \textit{StatevectorSimulator} from the IBM Quantum framework and the \textit{Local Simulator} from the Amazon Braket framework for the QSVM-Kernel results.
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002764310 8564_ $$82288808$$s212543$$uhttps://cds.cern.ch/record/2764310/files/HHyy.png$$y00001 Representative Feynman diagrams for (a) \ttH\ production, (b) \Hgamgam\ decay, and (c) non-resonant two-photon production. In these diagrams, $H$ denotes a Higgs boson, $g$ denotes a gluon, $q$ denotes a quark, $t$ denotes a top quark, $b$ denotes a bottom quark, $W$ denotes a W boson, and $\gamma$ denotes a photon.
002764310 8564_ $$82288809$$s320789$$uhttps://cds.cern.ch/record/2764310/files/ttH.png$$y00000 Representative Feynman diagrams for (a) \ttH\ production, (b) \Hgamgam\ decay, and (c) non-resonant two-photon production. In these diagrams, $H$ denotes a Higgs boson, $g$ denotes a gluon, $q$ denotes a quark, $t$ denotes a top quark, $b$ denotes a bottom quark, $W$ denotes a W boson, and $\gamma$ denotes a photon.
002764310 8564_ $$82288810$$s5166$$uhttps://cds.cern.ch/record/2764310/files/circuit-quantum-featuremap.png$$y00006 \textbf{(a)} Quantum circuit for evaluating the kernel entry for data events $\vec{x_i}$ and $\vec{x_j}$ used in our study. $H$ is a Hadamard gate and $U_{\Phi(\vec{x_i})}$ is a unitary operator that encodes data from a classical event in its parameters. \textbf{(b)} Quantum circuit of the unitary operator $U_{\Phi(\vec{x_i})}$. It is constituted by single-qubit rotation gates ($A$, $B$ and $A'$), as well as two-qubit CNOT entangling gates.
002764310 8564_ $$82288811$$s41272$$uhttps://cds.cern.ch/record/2764310/files/fig6a.png$$y00009 The AUC for various classifiers as a function of the \ttH\ analysis dataset size (10000 to 50000 events). (a) shows the results of the QSVM-Kernel (on the \textit{qsim Simulator} from the Google TensorFlow Quantum framework), the classical SVM and the classical BDT. (b) further shows the difference between the QSVM-Kernel algorithm and the classical algorithms. (c) shows the QSVM-Kernel results on the \textit{qsim Simulator} from the Google TensorFlow Quantum framework, the \textit{StatevectorSimulator} from the IBM Quantum framework and the \textit{Local Simulator} from the Amazon Braket framework. Here all the classifiers use the same 15 variables and the QSVM-Kernel classifiers employ 15 qubits on the quantum simulators. The quoted AUCs are averaged over 60 statistically independent datasets and the quoted errors are the standard deviations for the AUCs of the 60 datasets.
002764310 8564_ $$82288812$$s5142$$uhttps://cds.cern.ch/record/2764310/files/circuit-quantum-kernel.png$$y00005 \textbf{(a)} Quantum circuit for evaluating the kernel entry for data events $\vec{x_i}$ and $\vec{x_j}$ used in our study. $H$ is a Hadamard gate and $U_{\Phi(\vec{x_i})}$ is a unitary operator that encodes data from a classical event in its parameters. \textbf{(b)} Quantum circuit of the unitary operator $U_{\Phi(\vec{x_i})}$. It is constituted by single-qubit rotation gates ($A$, $B$ and $A'$), as well as two-qubit CNOT entangling gates.
002764310 8564_ $$82288813$$s43589$$uhttps://cds.cern.ch/record/2764310/files/fig2a.png$$y00007 ROC curves of various classifiers using the \ttH\ analysis datasets of 20000 events and 15 input variables. Each curve represents results averaged over 60 statistically independent datasets. (a) overlays the results of the QSVM-Kernel algorithm (on the \textit{qsim Simulator} from the Google TensorFlow Quantum framework), the classical SVM algorithm and the classical BDT algorithm. (b) overlays the QSVM-Kernel results on the \textit{qsim Simulator} from the Google TensorFlow Quantum framework, the \textit{StatevectorSimulator} from the IBM Quantum framework and the \textit{Local Simulator} from the Amazon Braket framework. Here the QSVM-Kernel classifiers employ 15 qubits on the quantum simulators.
002764310 8564_ $$82288814$$s45622$$uhttps://cds.cern.ch/record/2764310/files/fig2b.png$$y00008 ROC curves of various classifiers using the \ttH\ analysis datasets of 20000 events and 15 input variables. Each curve represents results averaged over 60 statistically independent datasets. (a) overlays the results of the QSVM-Kernel algorithm (on the \textit{qsim Simulator} from the Google TensorFlow Quantum framework), the classical SVM algorithm and the classical BDT algorithm. (b) overlays the QSVM-Kernel results on the \textit{qsim Simulator} from the Google TensorFlow Quantum framework, the \textit{StatevectorSimulator} from the IBM Quantum framework and the \textit{Local Simulator} from the Amazon Braket framework. Here the QSVM-Kernel classifiers employ 15 qubits on the quantum simulators.
002764310 8564_ $$82288815$$s41668$$uhttps://cds.cern.ch/record/2764310/files/fig7b.png$$y00014 AUCs of the QSVM-Kernel algorithm as a function of the number of qubits (10 to 20 qubits). The number of qubits is equal to the number of input variables. The 60 statistically independent \ttH\ analysis datasets of 20000 events are used in this study. In (a), we compare the results of the QSVM-Kernel classifier (on the \textit{qsim Simulator} from the Google TensorFlow Quantum framework) with the results of the classical SVM and classical BDT classifiers using the same input variables. In (b), we further display the difference between the QSVM-Kernel results and the classical machine learning results. In (c), we compare the \textit{qsim Simulator} from the Google TensorFlow Quantum framework, the \textit{StatevectorSimulator} from the IBM Quantum framework and the \textit{Local Simulator} from the Amazon Braket framework for the QSVM-Kernel results.
002764310 8564_ $$82288816$$s23829$$uhttps://cds.cern.ch/record/2764310/files/fig7c.png$$y00013 AUCs of the QSVM-Kernel algorithm as a function of the number of qubits (10 to 20 qubits). The number of qubits is equal to the number of input variables. The 60 statistically independent \ttH\ analysis datasets of 20000 events are used in this study. In (a), we compare the results of the QSVM-Kernel classifier (on the \textit{qsim Simulator} from the Google TensorFlow Quantum framework) with the results of the classical SVM and classical BDT classifiers using the same input variables. In (b), we further display the difference between the QSVM-Kernel results and the classical machine learning results. In (c), we compare the \textit{qsim Simulator} from the Google TensorFlow Quantum framework, the \textit{StatevectorSimulator} from the IBM Quantum framework and the \textit{Local Simulator} from the Amazon Braket framework for the QSVM-Kernel results.
002764310 8564_ $$82288817$$s35392$$uhttps://cds.cern.ch/record/2764310/files/fig6c.png$$y00010 The AUC for various classifiers as a function of the \ttH\ analysis dataset size (10000 to 50000 events). (a) shows the results of the QSVM-Kernel (on the \textit{qsim Simulator} from the Google TensorFlow Quantum framework), the classical SVM and the classical BDT. (b) further shows the difference between the QSVM-Kernel algorithm and the classical algorithms. (c) shows the QSVM-Kernel results on the \textit{qsim Simulator} from the Google TensorFlow Quantum framework, the \textit{StatevectorSimulator} from the IBM Quantum framework and the \textit{Local Simulator} from the Amazon Braket framework. Here all the classifiers use the same 15 variables and the QSVM-Kernel classifiers employ 15 qubits on the quantum simulators. The quoted AUCs are averaged over 60 statistically independent datasets and the quoted errors are the standard deviations for the AUCs of the 60 datasets.
002764310 8564_ $$82288818$$s40751$$uhttps://cds.cern.ch/record/2764310/files/fig6b.png$$y00011 The AUC for various classifiers as a function of the \ttH\ analysis dataset size (10000 to 50000 events). (a) shows the results of the QSVM-Kernel (on the \textit{qsim Simulator} from the Google TensorFlow Quantum framework), the classical SVM and the classical BDT. (b) further shows the difference between the QSVM-Kernel algorithm and the classical algorithms. (c) shows the QSVM-Kernel results on the \textit{qsim Simulator} from the Google TensorFlow Quantum framework, the \textit{StatevectorSimulator} from the IBM Quantum framework and the \textit{Local Simulator} from the Amazon Braket framework. Here all the classifiers use the same 15 variables and the QSVM-Kernel classifiers employ 15 qubits on the quantum simulators. The quoted AUCs are averaged over 60 statistically independent datasets and the quoted errors are the standard deviations for the AUCs of the 60 datasets.
002764310 8564_ $$82288819$$s19338$$uhttps://cds.cern.ch/record/2764310/files/fig10a.png$$y00016 ROC curve of the QSVM-Kernel classifier with the \textit{``ibmq\_paris''} quantum computer hardware using the \ttH\ analysis datasets of 100 events. For comparison, we overlay the ROC curve with the \textit{StatevectorSimulator} from the IBM Quantum framework using the same datasets. The results are averaged over the six hardware runs. All the QSVM-Kernel classifiers use 15 qubits and the same 15 variables.
002764310 8564_ $$82288820$$s32537$$uhttps://cds.cern.ch/record/2764310/files/paris_qubits.png$$y00015 The qubit map of the \textit{``ibmq\_paris''} quantum system~\cite{ibm_web}. The (darker) colors indicate (lower) readout error rates of the qubits and CNOT error rates of the connections. Our study uses qubits 3, 5, 8, 11, 14, 16, 19, 22, 25, 24, 23, 21, 18, 15 and 12.
002764310 8564_ $$82288821$$s68863$$uhttps://cds.cern.ch/record/2764310/files/fig11a.png$$y00017 ROC curve with the \textit{``ibmq\_paris''} quantum computer hardware and ROC curve with the \textit{StatevectorSimulator} from the IBM Quantum framework for each of the six hardware runs. Each run processes a statistically independent dataset of 100 events. All the QSVM-Kernel classifiers are using 15 qubits and the same 15 variables.
002764310 8564_ $$82321506$$s11932$$uhttps://cds.cern.ch/record/2764310/files/training_var_jet.png$$y00004 Signal and background distributions for some of the most powerful input variables to the \ttH\ analysis: $\textbf{(a)}$, the transverse momentum of the leading photon divided by the photon pair invariant mass, and $\textbf{(b)}$, the transverse momentum of the leading jet.
002764310 8564_ $$82321507$$s299431$$uhttps://cds.cern.ch/record/2764310/files/yy_background.png$$y00002 Representative Feynman diagrams for (a) \ttH\ production, (b) \Hgamgam\ decay, and (c) non-resonant two-photon production. In these diagrams, $H$ denotes a Higgs boson, $g$ denotes a gluon, $q$ denotes a quark, $t$ denotes a top quark, $b$ denotes a bottom quark, $W$ denotes a W boson, and $\gamma$ denotes a photon.
002764310 8564_ $$82321508$$s10841$$uhttps://cds.cern.ch/record/2764310/files/training_var_photon.png$$y00003 Signal and background distributions for some of the most powerful input variables to the \ttH\ analysis: $\textbf{(a)}$, the transverse momentum of the leading photon divided by the photon pair invariant mass, and $\textbf{(b)}$, the transverse momentum of the leading jet.
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