Hardware-Aware Tensor Networks for Real-Time Quantum-Inspired Anomaly Detection at Particle Colliders

Abstract

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.

Figures (9)

• Figure 1: Embedded particle MPS that represents the input to the SMPO and CSMPO models. $p_i$ refers to the physical dimension, here with a value of 3, and $b_0$ refers to the trivial bond dimension with value 1.
• Figure 2: Quantum Mutual Information between sites of the input MPS in the SMPO architecture, comparing ordering based on particle type and $p_\mathrm{T}$ (left) and spectral ordering (right). The use of spectral ordering ensures particles with high QMI are near each other in the SMPO structure, allowing for reduced bond dimensions to capture correlations between inputs.
• Figure 3: Diagram of the SMPO model used in this work, where $b$ refers to the bond dimension and has a value of 4, $p_i$ refers to input physical dimension with a value of 3, and $p_o$ refers to the physical output dimension with a value of 3. The shaded node refers to the site in the SMPO with a physical output leg.
• Figure 4: Diagram of the CSMPO model used in this work, where $b_1$ and $b_2$ refer to the bond dimensions of the first and second layers respectively with values $b_1$ = $b_2$ = 2, $p_i$ refers to input physical dimension with a value of 3, $p'$ refers to physical dimension of the intermediate MPS created between the two layers with a value of 3, and $p_o$ refers to the output physical dimension with a value of 3. The shaded nodes refer to the sites in the CSMPO layers with physical output legs.
• Figure 5: ROC curve for the SMPO model, indicating AUC and TPR for all four test signals. The error band reflects the ensembled performance of ten identical model trainings with different random seeds. The solid line indicates the best performing model in the ensemble.