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 & tables
Figure 1: Embedded particle MPS that represents the input to the SMPO and CSMPO models. pi refers to the physical dimension, here with a value of 3, and b0 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 pT (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, pi refers to input physical dimension with a value of 3, and po 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 b1 and b2 refer to the bond dimensions of the first and second layers respectively with values b1 = b2 = 2, pi 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 po 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.
Figure 6: ROC curve for the CSMPO 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.
Model
Signal
Metric
AUC [%]
TPR [%]
SMPO
A→4ℓ
0.90
6.35
h±→τν
0.88
0.10
h0→ττ
0.80
0.11
LQ →bτ
0.86
0.10
CSMPO 19→7→1
A→4ℓ
0.89
2.94
Table 1: Performance for the SMPO and CSMPO models assessed by two metrics, AUC and TPR at FPR = 10 -5 , for the four test signals, considering the best model in the ensemble.
Figure 7: Impact of quantizing model inputs and weights to several fixed-point levels on ∣∣MPS∣∣2 normalized distribution of the background testing events (left), as well as AUC and TPR (right).
Figure 8: Tensor contraction steps in the implementation of the SMPO model application on an input event. The first step is the vertical contraction along the physical output legs of the input embedded MPS and the physical input legs of the SMPO (a). The horizontal contraction is implemented as a bi-directional contraction chain (b) - (e) between the extreme sites (shaded in green) and their neighbor. The remaining three sites are contracted together (f) to yield the final vector site, which is contracted with itself (g) to yield the squared norm ∥MPS∥2 .
Figure 9: Tensor contraction steps in the implementation of the CSMPO model application on an input event. The first step is the vertical contraction along the physical output legs of the input embedded MPS and the physical input legs of the first layer of the CSMPO (a). Sites without physical output legs (shaded in blue) are contracted with each other (b) followed by contraction to their right neighbor (c). The 7-site MPS created at this stage is vertically contracted with the second layer of the CSMPO (d), followed by a bi-directional contraction chain (e) - (g) between the extreme sites (shaded in green) and their neighbor. The remaining three sites are contracted together (h) to yield the final vector site, which is contracted with itself (i) to yield the squared norm ∥MPS∥2 .
Model
SMPO
CSMPO 19→7→1
CSMPO 19→2→1
# Parameters
936
456
264
# MACs
1255
1039
455
LUTs
76669
143754
100146
FFs
9817
8272
4870
DSPs
0
0
0
Latency [ μ s]
0.37
0.33
0.24
Table 2: Model details, namely number of trainable parameters and number of multiply-and-accumulate (MAC) operations for inference, along with FPGA resources (expressed in LUTs, DSPs, FFs, and latency) comparing the SMPO and CSMPO model benchmarks.
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.
Apimuk Sornsaeng, Si Min Chan, Wenxuan Zhang +4
Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore · Centre for Quantum Technologies, National University of Singapore 117543, Singapore · Artificial Intelligence and Data Analytics Strategic Technology Centre, ST Engineering +2
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.
Ivan Ge, Sagar Addepalli, Abhilasha Dave +1
Department of Physics, Stanford University, 450 Jane Stanford Way, Stanford, 94305, CA, USA. · SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, 94025, CA, USA.
We investigate whether a multiscale tensor-network architecture can provide a useful inductive bias for reconstruction-based anomaly detection in collider jets. Jets are produced by a branching cascade, so their internal structure is naturally organised across angular and momentum scales. This motivates an autoencoder that compresses information hierarchically and can reorganise short-range correlations before coarse-graining. Guided by this picture, we formulate a MERA-inspired autoencoder acting directly on ordered jet constituents. To the best of our knowledge, a MERA-inspired autoencoder has not previously been proposed, and this architecture has not been explored in collider anomaly detection. We compare this architecture to a dense autoencoder, the corresponding tree-tensor-network limit, and standard classical baselines within a common background-only reconstruction framework. The paper is organised around two main questions: whether locality-aware hierarchical compression is genuinely supported by the data, and whether the disentangling layers of MERA contribute beyond a simpler tree hierarchy. To address these questions, we combine benchmark comparisons with a training-free local-compressibility diagnostic and a direct identity-disentangler ablation. The resulting picture is that the locality-preserving multiscale structure is well matched to jet data, and that the MERA disentanglers become beneficial precisely when the compression bottleneck is strongest. Overall, the study supports locality-aware hierarchical compression as a useful inductive bias for jet anomaly detection.
Emre Gurkanli, Michael Spannowsky
Department of Physics, Sinop University, Turkiye · Institute for Theoretical Physics, Campus Süd, Karlsruhe Institute of Technology (KIT), D-76128 Karlsruhe, Germany · Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, Karlsruhe 76131, Germany