Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States

Abstract

Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine learning techniques, thereby facilitating an improved interpretability of neural networks. This study presents the discrimination of top quark signal over QCD background processes using a Matrix Product State classifier. We show that entanglement entropy can be used to interpret what a network learns, which can be used to reduce the complexity of the network and feature space without loss of generality or performance. For the optimisation of the network, we compare the Density Matrix Renormalization Group (DMRG) algorithm to stochastic gradient descent (SGD) and propose a joined training algorithm to harness the explainability of DMRG with the efficiency of SGD.

Tensor networks for quantum machine learning

“…Applications in ML can be found for a wide variety of tasks. In image analysis, TN-based ML models are used for classification [50,73,74], compression [75] or feature extraction [66,76]. TNbased regressors have been successfully applied to nonlinear system identification [15] where the task is to generate a model of a nonlinear system from its behaviour.…”

Machine Learning of Average Non-Markovianity from Randomized Benchmarking

“…The use of MPOs has already proven useful for the numerical and conceptual investigation of open quantum systems, e.g., in [34,[36][37][38][39], and are still an active subject of investigation. Tensor networks, of which MPOs are particular cases, naturally find applications for machine learning tasks [23,[40][41][42][43][44][45][46], and can further serve to learn full process tensors [47]. Here we show a way to train a model that allows to learn the effective average non-Markovianity from a RB experiment's data.…”

Quantum anomaly detection for collider physics

“…In this paper, QML refers to machine learning tasks that are executed on quantum computing hardware. While QML is not known to be more efficient than classical machine learning (CML), there have been many empirical studies to explore the potential of QML for HEP [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] (see also ref. [20] for a recent review).…”