Towards Tensor Network Models for Low-Latency Jet Tagging on FPGAs

TL;DR

This paper investigates real-time jet tagging at HL-LHC Level-1 trigger using Tensor Network models (MPS and TTN) implemented on FPGAs for ultra-low-latency inference. It introduces physics-informed per-particle embeddings and employs quantum mutual information to optimize feature layout, achieving competitive full-precision performance across jet constituents. Through post-training quantization studies and FPGA synthesis, the work demonstrates sub-microsecond latency and manageable hardware resources, showing TNs as viable, interpretable alternatives to deep networks for trigger-level inference. The results support broader deployment of TN-based architectures in low-latency, resource-constrained environments and outline directions for further compression and gauge-aware quantization.

Abstract

We present a systematic study of Tensor Network (TN) models $\unicode{x2013}$ Matrix Product States (MPS) and Tree Tensor Networks (TTN) $\unicode{x2013}$ for real-time jet tagging in high-energy physics, with a focus on low-latency deployment on Field Programmable Gate Arrays (FPGAs). Motivated by the strict requirements of the HL-LHC Level-1 trigger system, we explore TNs as compact and interpretable alternatives to deep neural networks. Using low-level jet constituent features, our models achieve competitive performance compared to state-of-the-art deep learning classifiers. We investigate post-training quantization to enable hardware-efficient implementations without degrading classification performance or latency. The best-performing models are synthesized to estimate FPGA resource usage, latency, and memory occupancy, demonstrating sub-microsecond latency and supporting the feasibility of online deployment in real-time trigger systems. Overall, this study highlights the potential of TN-based models for fast and resource-efficient inference in low-latency environments.

Figures (7)

• Figure 1: Pipeline of the systematic study consisting of: (1) data embedding procedure embedding each particle $x_i$ ($i \in (1, N)$) with feature map $\phi$ into a product of embedded vectors, (2) Tensor Network model(s) implemented and run on FPGA, (3) performance evaluation in terms of classification accuracy, the area under the receiver operating characteristic curve and relevant hardware metrics. $N$ is the number of particles in a jet. $C$ is an output vector that is used to obtain class probabilities.
• Figure 2: Quantum mutual information between pairs of inputs of a TN model. (a) TN model trained on $N=16$ constituents per jet, embedding $p_T$ and $\Delta R$ of each particle in adjacent sites. (b) TN model trained on the same dataset, where features are permuted so that $p_T$ of all particles come first, followed by $\Delta R$.
• Figure 3: Matrix Product State (MPS) structure with five tensors connected via bond indices of dimension $D$, where each tensor has a physical dimension $d$. The central tensor has an additional output leg corresponding to the class index $C$.
• Figure 4: Tree Tensor Network (TTN) approximating a $8$-order tensor with three layers $l$, bond dimension $D_l$ for each layer and output index $C$ with dimension corresponding to the number of classes.
• Figure 5: Examples of TTN (top) and MPS (bottom) inference algorithms, considering $N=4$ particles. Black arrows correspond to parallel contractions, while gray arrows link different sequential steps.