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

Sagar Addepalli; Prajita Bhattarai; Abhilasha Dave; Julia Gonski

cs.LGMar 27, 2026

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

Authors: Sagar Addepalli, Prajita Bhattarai, Abhilasha Dave, Julia Gonski

Organizations: SLAC National Accelerator Laboratory, 2575 Sand Hill Rd, Menlo Park, 94025, CA, USA.

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 & tables

Panel of Figure 1 — 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.

Panel of Figure 2 — 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.

Panel of Figure 3 — 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.

Panel of Figure 4 — 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, $p^{\prime}$ 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.

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
Model	Signal	AUC [%]	TPR [%]
SMPO	$A\rightarrow 4\ell$	0.90	6.35
	$h^{\pm}\rightarrow\tau\nu$	0.88	0.10
	$h^{0}\rightarrow\tau\tau$	0.80	0.11
	LQ $\rightarrow b\tau$	0.86	0.10
CSMPO 19→7→1	$A\rightarrow 4\ell$	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.

Panel of Figure 7 — Figure 7: Impact of quantizing model inputs and weights to several fixed-point levels on $||\mathbf{MPS}||^{2}$ normalized distribution of the background testing events (left), as well as AUC and TPR (right).

Panel of Figure 8 — 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 $\|\mathbf{MPS}\|^{2}$ .

Panel of Figure 9 — 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 $\|\mathbf{MPS}\|^{2}$ .

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 [ $\mu$ 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.

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Site(s)	Elements	MACs
0	$1\times 1\times 4=4$	12
1–8	$8\times 1\times 4\times 4=128$	384
9	$3\times 4\times 4=48$	144
10–17	$8\times 1\times 4\times 4=128$	384
18	$1\times 4\times 1=4$	12
Subtotal		936

Appendix

Table 12

Component	Formula	MACs
Left sweep	$8\times b^{2}$	128
Right sweep	$8\times b^{2}$	128
Merge pass 1: $rc[p][l]=\sum_{r}T_{9}[p][l][r]\cdot\texttt{right\_env}[r]$	$p_{o}\times b\times b$	48
Merge pass 2: $\texttt{output}[p]=\sum_{l}\texttt{left\_env}[l]\cdot rc[p][l]$	$p_{o}\times b$	12
Subtotal		316

Appendix

Table 13

Inference step	MACs
Vertical	936
Horizontal	316
Norm	3
Total	1255

Appendix

Table 3: MAC count by inference step for the SMPO model.

Site(s)	Role	Elements	MACs
0	Left boundary, output	$3\times 1\times 2=6$	18
1–17	Interior, non-output	$17\times 1\times 2\times 2=68$	204
18	Right boundary, output	$3\times 2\times 1=6$	18
Subtotal			240

Appendix

Table 4:

M=2

, outputs at

\{0,\,18\}

Site(s)	Role	Elements	MACs
0	Left boundary, output	6	18
1–2	Interior, non-output	8	24
3	Interior, output	12	36
4–5	Interior, non-output	8	24
6	Interior, output	12	36
7–8	Interior, non-output	8	24

Appendix

Table 5:

M=7

, outputs at

\{0,\,3,\,6,\,9,\,12,\,15,\,18\}

Group	Sites	$g$	Chain MACs	Absorb MACs	Total
$0\to 18$	1–17	17	128	24	152
Subtotal					152

Appendix

Table 6:

M=2

, 1 group (

g=17

)

Group	Sites	$g$	Chain MACs	Absorb MACs	Total
$0\to 3$	1, 2	2	8	24	32
$3\to 6$	4, 5	2	8	24	32
$6\to 9$	7, 8	2	8	24	32
$9\to 12$	10, 11	2	8	24	32
$12\to 15$	13, 14	2	8	24	32
$15\to 18$	16, 17	2	8	24	32

Appendix

Table 7:

M=7

, 6 groups

Site	$p_{\text{out},\text{eff}}$	$B_{L}$	$B_{R}$	Elements	MACs
0 (output, left boundary)	3	4	1	12	36
1 (non-output, right boundary)	1	1	4	4	12
Subtotal					48

Appendix

Table 8:

M=2

(output at site 0)

Site	$p_{\text{out},\text{eff}}$	$B_{L}$	$B_{R}$	Elements	MACs
0 (non-output, left boundary)	1	1	4	4	12
1 (non-output, interior)	1	4	4	16	48
2 (non-output, interior)	1	4	4	16	48
3 (output, interior)	3	4	4	48	144
4 (non-output, interior)	1	4	4	16	48
5 (non-output, interior)	1	4	4	16	48

Appendix

Table 9:

M=7

(output at site 3)

Component	Formula	MACs
Left sweep	0 steps	0
Right sweep	0 steps	0
Merge: $\texttt{output}[p]=\sum_{r}T_{1}[p][0][r]\cdot\texttt{right\_env}[r]$	$p_{o}\times B$	12
Subtotal		12

Appendix

Table 10:

M=2

(output at site 1). Left wing: site 0 only (boundary init, 0 sweep steps). Right wing: none (output is left boundary).

Component	Formula	MACs
Left sweep	$2\times B^{2}$	32
Right sweep	$2\times B^{2}$	32
Merge pass 1	$p_{o}\times B^{2}$	48
Merge pass 2	$p_{o}\times B$	12
Subtotal		124

Appendix

Table 11:

M=7

(output at site 3). Left wing: sites 0 (init), 1, 2 (sweep)

\to

2 sweep steps. Right wing: sites 6 (init), 5, 4 (sweep)

\to

2 sweep steps.

Component	$M=2$	$M=7$	Single
L1 Vertical	240	360	936
L1 Horizontal	152	192	—
L2 Vertical	48	360	—
L2 Horizontal	12	124	316
Norm	3	3	3
Total	455	1039	1255

Appendix

Table 23

Explore similar work

SMT-AD: a scalable quantum-inspired anomaly detection approach
Apr 7, 2026Apimuk Sornsaeng, Si Min Chan, Wenxuan Zhang +4Anomaly Detection Quantum-Inspired ML
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
Classical Hardware Acceleration of Quantum Autoencoders for Real-Time Anomaly Detection in Collider Experiments
Jul 22, 2026Ivan Ge, Sagar Addepalli, Abhilasha Dave +1Online Anomaly Detection Quantum Machine Learning
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.
Quantum-Inspired Tensor Network Autoencoders for Anomaly Detection: A MERA-Based Approach
Apr 8, 2026Emre Gurkanli, Michael SpannowskyAnomaly Detection Autoencoders
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

Apr 7, 2026J/K move · Enter open · S save

SMT-AD: a scalable quantum-inspired anomaly detection approach

Apimuk Sornsaeng, Si Min Chan, Wenxuan Zhang, Swee Liang Wong+3

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

Anomaly Detection Quantum-Inspired ML

Open paper AskPDF arXiv

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

Explore similar work

SMT-AD: a scalable quantum-inspired anomaly detection approach

Classical Hardware Acceleration of Quantum Autoencoders for Real-Time Anomaly Detection in Collider Experiments

Quantum-Inspired Tensor Network Autoencoders for Anomaly Detection: A MERA-Based Approach