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Solving a Higgs optimization problem with quantum annealing for machine learning

Abstract

The discovery of Higgs-boson decays in a background of standard-model processes was assisted by machine learning methods1,2. The classifiers used to separate signals such as these from background are trained using highly unerring but not completely perfect simulations of the physical processes involved, often resulting in incorrect labelling of background processes or signals (label noise) and systematic errors. Here we use quantum3,4,5,6 and classical7,8 annealing (probabilistic techniques for approximating the global maximum or minimum of a given function) to solve a Higgs-signal-versus-background machine learning optimization problem, mapped to a problem of finding the ground state of a corresponding Ising spin model. We build a set of weak classifiers based on the kinematic observables of the Higgs decay photons, which we then use to construct a strong classifier. This strong classifier is highly resilient against overtraining and against errors in the correlations of the physical observables in the training data. We show that the resulting quantum and classical annealing-based classifier systems perform comparably to the state-of-the-art machine learning methods that are currently used in particle physics9,10. However, in contrast to these methods, the annealing-based classifiers are simple functions of directly interpretable experimental parameters with clear physical meaning. The annealer-trained classifiers use the excited states in the vicinity of the ground state and demonstrate some advantage over traditional machine learning methods for small training datasets. Given the relative simplicity of the algorithm and its robustness to error, this technique may find application in other areas of experimental particle physics, such as real-time decision making in event-selection problems and classification in neutrino physics.

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Figure 1: Representative Feynman diagrams of processes that contribute to the simulated distributions of the Higgs signal and of the background standard-model processes.
Figure 2: Distributions of the eight kinematic variables used to construct weak classifiers.
Figure 3: Receiver operating characteristic (ROC) curves for the annealer-trained networks with f = 0.05, the DNN and XGB.
Figure 4: Area under the ROC curve (AUROC) for the annealer-trained networks with f = 0.05, the DNN and XGB.
Figure 5: Difference between the AUROCs for different algorithms.

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Acknowledgements

This project is supported in part by the United States Department of Energy, Office of High Energy Physics Research Technology Computational HEP and Fermi Research Alliance, LLC under contract no. DE-AC02-07CH11359. The project is also supported in part under ARO grant number W911NF-12-1-0523 and NSF grant number INSPIRE-1551064. The work is supported in part by the AT&T Foundry Innovation Centers through INQNET, a programme for accelerating quantum technologies. We thank the Advanced Scientific Computing Research programme of the DOE for the opportunity to present and discuss this work at the ASCR workshop on Quantum Computing for Science (2015). We acknowledge the funding agencies and all of the scientists and staff at CERN and internationally whose hard work resulted in the momentous H(125) discovery in 2012.

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Contributions

A.M. mapped the problem on the D-Wave software architecture, analysed the data, provided the machine learning methodology and, with M.S., provided knowledge of Higgs physics. J.J. provided quantum and simulated annealing research, data analysis, machine learning work and, with D.L., quantum and simulated annealing knowledge. J.-R.V. provided quantum annealing research, data analysis, machine learning methods and error analysis, with J.J. D.L. and M.S. oversaw the work, data analysis and results. D.L. conceived the quantum machine learning methodology. M.S. conceived the application. All authors contributed to writing and reviewing the manuscript.

Corresponding author

Correspondence to Maria Spiropulu.

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The authors declare no competing financial interests.

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Reviewer Information Nature thanks S. Zohren and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Mott, A., Job, J., Vlimant, JR. et al. Solving a Higgs optimization problem with quantum annealing for machine learning. Nature 550, 375–379 (2017). https://doi.org/10.1038/nature24047

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