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arXiv:2004.13747 · npj Quantum Information

Quantum-inspired machine learning on high-energy physics data

Timo Felser, Marco Trenti, L. Sestini, A. Gianelle, D. Zuliani, Donatella Lucchesi, Simone Montangero

Published Jul 15, 2021• 47 citations
arXivHTMLPDF

Abstract

Abstract Tensor Networks, a numerical tool originally designed for simulating quantum many-body systems, have recently been applied to solve Machine Learning problems. Exploiting a tree tensor network, we apply a quantum-inspired machine learning technique to a very important and challenging big data problem in high-energy physics: the analysis and classification of data produced by the Large Hadron Collider at CERN. In particular, we present how to effectively classify so-called b-jets, jets originating from b-quarks from proton–proton collisions in the LHCb experiment, and how to interpret the classification results. We exploit the Tensor Network approach to select important features and adapt the network geometry based on information acquired in the learning process. Finally, we show how to adapt the tree tensor network to achieve optimal precision or fast response in time without the need of repeating the learning process. These results pave the way to the implementation of high-frequency real-time applications, a key ingredient needed among others for current and future LHCb event classification able to trigger events at the tens of MHz scale.

DOI
10.1038/s41534-021-00443-w

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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.
We describe a quantum-assisted machine learning method in which multivariate data are encoded into quantum states in a Hilbert space whose dimension is exponentially large in the length of the data vector. Learning in this space occurs through applying a low-depth quantum circuit with a tree-tensor-network (TTN) topology acting as an unsupervised feature extractor to identify the most relevant quantum states in a data-driven fashion and then applying a supervised linear classifier encoding the class decision in a small-dimensional quantum register. We present tools for making TTN classifiers amenable to implementation on gate-based quantum computing devices, including an embedding map with accuracy similar to the recently defined exponential machines (A. Novikov et al., arXiv:1605.03795) but which produces valid quantum state embeddings of classical data vectors, and the use of manifold-based gradient optimization schemes to produce isometric operations mapping quantum states to a register of qubits defining a class decision. We detail methods for efficiently obtaining one-point and two-point correlation functions of the vectors defining the decision boundary of the quantum model, which can be used for model interpretability, as well as methods for obtaining classification decisions from partial data vectors. Further, we show that the use of isometric tensors can significantly aid in the human interpretability of the correlation functions extracted from the decision weights and may produce models that are less susceptible to adversarial perturbations. Finally, we discuss in detail the problem of compiling classically optimized isometric TTN models into unitary operations to be run on quantum computers and how isometric models requiring postselection on quantum hardware can be used to precondition variational Ans\"atze for models without postselection. We demonstrate our methodologies in applications utilizing the MNIST database of handwritten digits and a multivariate time-series data set of human activity recognition.
Some of the most significant achievements of the modern era of particle physics, such as the discovery of the Higgs boson, have been made possible by the tremendous effort in building and operating large-scale experiments like the Large Hadron Collider or the Tevatron. In these facilities, the ultimate theory to describe matter at the most fundamental level is constantly probed and verified. These experiments often produce large amounts of data that require storing, processing, and analysis techniques that continually push the limits of traditional information processing schemes. Thus, the High-Energy Physics (HEP) field has benefited from advancements in information processing and the development of algorithms and tools for large datasets. More recently, quantum computing applications have been investigated to understand how the community can benefit from the advantages of quantum information science. Nonetheless, to unleash the full potential of quantum computing, there is a need to understand the quantum behavior and, thus, scale up current algorithms beyond what can be simulated in classical processors. In this work, we explore potential applications of quantum machine learning to data analysis tasks in HEP and how to overcome the limitations of algorithms targeted for Noisy Intermediate-Scale Quantum (NISQ) devices.
High-energy colliders, such as the Large Hadron Collider (LHC) at CERN, are genuine quantum machines, so, in line with Richard Feynman's original motivation for Quantum Computing, the scattering processes that take place there are natural candidates to be simulated on a quantum system. Potential applications range from quantum machine learning methods for collider data analysis, to faster and more precise evaluations of intricate multiloop Feynman diagrams, more efficient jet clustering, improved simulations of parton showers, and many other tasks. In this work, the focus will be on two specific applications: first, the identification of the causal structure of multiloop vacuum amplitudes, a key ingredient of the Loop-Tree Duality and an area with deep connections to graph theory; and second, the integration and sampling of high-dimensional functions. The latter constitutes a first step toward the realization of a fully fledged quantum event generator operating at high perturbative orders.
Abstract Machine Learning algorithms have played an important role in hadronic jet classification problems. The large variety of models applied to Large Hadron Collider data has demonstrated that there is still room for improvement. In this context Quantum Machine Learning is a new and almost unexplored methodology, where the intrinsic properties of quantum computation could be used to exploit particles correlations for improving the jet classification performance. In this paper, we present a brand new approach to identify if a jet contains a hadron formed by a b or b‾ \overline{b} b b ¯ quark at the moment of production, based on a Variational Quantum Classifier applied to simulated data of the LHCb experiment. Quantum models are trained and evaluated using LHCb simulation. The jet identification performance is compared with a Deep Neural Network model to assess which method gives the better performance.