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.

arXiv comment29 pages, 15 figures. Accepted version for publication in JHEP

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• Tensor networks for quantum machine learning
• Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data
• Quantum-probabilistic Hamiltonian learning for generative modelling & anomaly detection
• Towards a Quantum Simulation of Nonlinear Sigma Models with a Topological Term
• Jet Discrimination with Quantum Complete Graph Neural Network
• Machine learning with tree tensor networks, CP rank constraints, and tensor dropout
• Survey on Computational Applications of Tensor Network Simulations
• Quantum clustering and jet reconstruction at the LHC
• Tensor Network for Anomaly Detection in the Latent Space of Proton Collision Events at the LHC
• Using matrix-product states for time-series machine learning