Quantum machine learning offers the ability to capture complex correlations in high-dimensional feature spaces, crucial for the challenge of detecting beyond the Standard Model physics in collider events, along with the potential for unprecedented computational efficiency in future quantum processors. Near-term utilization of these benefits can be achieved by developing quantum-inspired algorithms for deployment in classical hardware to enable applications at the "edge" of current scientific experiments. This work demonstrates the use of tensor networks for real-time anomaly detection in collider detectors. A spaced matrix product operator (SMPO) is developed that provides sensitivity to a variety beyond the Standard Model benchmarks, and can be implemented in field programmable gate array hardware with resources and latency consistent with trigger deployment. The cascaded SMPO architecture is introduced as an SMPO variation that affords greater flexibility and efficiency in ways that are key to edge applications in resource-constrained environments. These results reveal the benefit and near-term feasibility of deploying quantum-inspired ML in high energy colliders.
Quantum machine learning offers the ability to capture complex correlations in high-dimensional feature spaces, crucial for the challenge of detecting beyond the Standard Model physics in collider events, along with the potential for unprecedented computational efficiency in future quantum processors. Near-term utilization of these benefits can be achieved by developing quantum-inspired algorithms for deployment in classical hardware to enable applications at the "edge" of current scientific experiments. This work demonstrates the use of tensor networks for real-time anomaly detection in collider detectors. A spaced matrix product operator (SMPO) is developed that provides sensitivity to a variety beyond the Standard Model benchmarks, and can be implemented in field programmable gate array hardware with resources and latency consistent with trigger deployment. The cascaded SMPO architecture is introduced as an SMPO variation that affords greater flexibility and efficiency in ways that are key to edge applications in resource-constrained environments. These results reveal the benefit and near-term feasibility of deploying quantum-inspired ML in high energy colliders.
Quantum machine learning (QML) algorithms in high energy physics (HEP) can efficiently represent and leverage long-range, high-order correlations in high-dimensional collider data, potentially with fewer parameters and favorable scaling relative to classical models. Deployment of QML in real-time collider applications such as trigger systems requires the ability to emulate and compile quantum circuits classically, then synthesize the resulting quantum gates onto low-latency hardware accelerators, namely field-programmable gate arrays (FPGAs). We present a study of variational quantum autoencoder models for real-time anomaly detection triggers in modern collider experiments. The models achieve performance comparable to state-of-the-art classical approaches and, after FPGA synthesis, satisfy resource usage and timing constraints consistent with trigger applications in future colliders. This work provides one of the first FPGA implementations of QML models for HEP triggers, enabling higher-capability models in today's classical data acquisition pipelines while advancing quantum readiness of collider experiment infrastructure.
Abstract Tensor networks (TNs) are a computational paradigm used for representing quantum many-body systems. Recent works have shown how TNs can also be applied to perform machine learning (ML) tasks, yielding comparable results to standard supervised learning techniques. In this work, we study the use of Tree TNs (TTNs) in high-frequency real-time applications by exploiting the low-latency hardware of the field-programmable gate array (FPGA) technology. We present different implementations of TTN classifiers, capable of performing inference on classical ML datasets as well as on complex physics data. A preparatory analysis of bond dimensions and weight quantization is realized in the training phase, together with entanglement entropy and correlation measurements, that help setting the choice of the TTN architecture. The generated TTNs are then deployed on a hardware accelerator; using an FPGA integrated into a server, the inference of the TTN is completely offloaded. Eventually, a classifier for high energy physics applications is implemented and executed fully pipelined with sub-microsecond latency.
Abstract Machine learning is a promising application of quantum computing, but challenges remain for implementation today because near-term devices have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine learning in the classical context, we propose quantum computing approaches to both discriminative and generative learning, with circuits based on tree and matrix product state tensor networks, that could already have benefits with such near-term devices. The result is a unified framework in which classical and quantum computing can benefit from the same theoretical and algorithmic developments, and the same model can be trained classically then transferred to the quantum setting for additional optimization. Tensor network circuits can also provide qubit-efficient schemes in which, depending on the architecture, the number of physical qubits required scales only logarithmically with, or independently of the input or output data sizes. We demonstrate our proposals with numerical experiments, training a discriminative model to perform handwriting recognition using a hybrid quantum-classical optimization procedure that could be carried out on quantum hardware today, and testing the noise resilience of the trained model.
Quantum-inspired tensor networks algorithms have shown to be effective and efficient models for machine learning tasks, including anomaly detection. Here, we propose a highly parallelizable quantum-inspired approach which we call SMT-AD from Superposition of Multiresolution Tensors for Anomaly Detection. It is based upon the superposition of bond-dimension-1 matrix product operators to transform the input data with Fourier-assisted feature embedding, where the number of learnable parameters grows linearly with feature size, embedding resolutions, and the number of additional components in the matrix product operators structure. We demonstrate successful anomaly detection when applied to standard datasets, including credit card transactions, and find that, even with minimal configurations, it achieves competitive performance against established anomaly detection baselines. Furthermore, it provides a straightforward way to reduce the weight of the model and even improve the performance by highlighting the most relevant input features.
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.
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.