Tensor Network for Anomaly Detection in the Latent Space of Proton Collision Events at the LHC

TL;DR

This work introduces a quantum-inspired tensor-network approach using a continuous-valued Matrix Product State (MPS) to perform anomaly detection in the latent space produced by an autoencoder for LHC dijet events. By embedding continuous latent features with an isometric Laguerre feature map, the model learns the Standard Model distribution P(x)=|<Phi(x)|Psi>|^2 and flags low-probability events as anomalies, enabling real-time scoring. Through a systematic hyperparameter study, the Laguerre embedding with a unitary initializer achieves robust training and strong signal-background separation, with notable gains over quantum kernel methods for certain new-physics scenarios (e.g., BR G→WW with AUC ≈ 69.5%). Inference times are under 100 ms per event, supporting potential deployment in the High-Level Trigger, and the results emphasize the practicality of quantum-inspired TNs for online anomaly detection in collider experiments.

Abstract

The pursuit of discovering new phenomena at the Large Hadron Collider (LHC) demands constant innovation in algorithms and technologies. Tensor networks are mathematical models on the intersection of classical and quantum machine learning, which present a promising and efficient alternative for tackling these challenges. In this work, we propose a tensor network-based strategy for anomaly detection at the LHC and demonstrate its superior performance in identifying new phenomena compared to established quantum methods. Our model is a parametrized Matrix Product State with an isometric feature map, processing a latent representation of simulated LHC data generated by an autoencoder. Our results highlight the potential of tensor networks to enhance new-physics discovery.

Figures (9)

• Figure 1: Anomaly detection pipeline: Proton-proton collision data ($n$ samples with $p_T, \Delta\eta, \Delta\phi$ features) is passed through an encoder, generating $M$ latent features mapped by isometric feature functions into a product state contracted with an MPS model with $A_k$ trainable parameters (purple circle). The MPS, trained on SM samples via NLL loss minimization, is evaluated both on SM and BSM events. Performance is measured using output probabilities as anomaly scores and metrics from the Receiver Operating Characteristic (ROC) curve (Area Under the Curve (AUC) value and background efficiency, $\varepsilon_b$, at a given signal efficiency, $\varepsilon_s$).
• Figure 2: Graphical representation of a quantum state $|\Psi\rangle$ decomposed to an MPS with physical indices $t_k$ and bond indices $\chi_k$.
• Figure 3: Graphical representation of the continuous-valued MPS model used for anomaly detection, consisting of a product state $\Phi(\mathbf{x})$ (feature layer), and a parametrized MPS $|\Psi\rangle$ with $A_k$ elements (TN layer).
• Figure 4: Negative Log Likelihood loss as a function of the training epoch for each initializer and bond dimension $\chi$ using a Legendre feature map of degree two.
• Figure 5: Comparison of anomaly scores for QCD (background) and BSM (anomaly) across different embedding polynomial functions - Laguerre (left), Legendre (center), and Hermite (right) for latent space $l=4$. Each distribution corresponds to a different bond dimension $\chi \in {2, 4, 8, 16}$. The solid line style visualizes QCD distribution, and the filled histogram is for BSM.