Quantum anomaly detection in the latent space of proton collision events at the LHC

TL;DR

This work investigates unsupervised quantum machine learning for anomaly detection in LHC proton–proton collision data by projecting high-dimensional jet information into a latent space with a classical autoencoder and applying quantum kernel methods and quantum clustering to identify potential new physics. The approach systematically analyzes how quantum resources, particularly the number of qubits $n_q$ and circuit depth $L$, as well as entanglement, affect anomaly-detection performance, demonstrating regimes where a quantum kernel machine can outperform the best classical kernel. Hardware feasibility is shown by a running example on IBM Q Toronto with eight qubits, achieving near-ideal performance for moderate circuit depths and confirming that entanglement is a key resource for the observed advantage. The results highlight a realistic path toward quantum-accelerated, model-independent searches for new phenomena at the LHC, while acknowledging limitations and outlining future directions such as data-biased inductive design and broader classical baselines.

Abstract

The ongoing quest to discover new phenomena at the LHC necessitates the continuous development of algorithms and technologies. Established approaches like machine learning, along with emerging technologies such as quantum computing show promise in the enhancement of experimental capabilities. In this work, we propose a strategy for anomaly detection tasks at the LHC based on unsupervised quantum machine learning, and demonstrate its effectiveness in identifying new phenomena. The designed quantum models, an unsupervised kernel machine and two clustering algorithms, are trained to detect new-physics events using a latent representation of LHC data, generated by an autoencoder designed to accommodate current quantum hardware limitations on problem size. For kernel-based anomaly detection, we implement an instance of the model on a quantum computer, and we identify a regime where it significantly outperforms its classical counterparts. We show that the observed performance enhancement is related to the quantum resources utilised by the model.

Figures (8)

• Figure 1: Classical-quantum pipeline. LHC collision data (simulation) are passed through an autoencoder for dimensionality reduction followed by the quantum anomaly detection models: unsupervised quantum kernel machine and quantum clustering algorithms (QK-means/QK-medians). Each jet contains 100 particles, each particle is described by three features $(\Delta\eta, \Delta\phi, p_T)$ where $\Delta$ represents a distance from the jet axis. Hence, a dijet collision event is described by 300 features. The quantum models are trained on Standard Model data and learn to recognise anomalies in unseen data. All models are evaluated by calculating the Receiver Operating Characteristic (ROC) curve and metrics appropriate for anomaly detection tasks, and are compared to their classical counterparts (see "Evaluation of model performance" subsection in the Results).
• Figure 1: Characterization metrics of the data encoding circuit. The metrics are calculated via sampling the circuit parameters from three different distributions as depicted in the legends: the uniform distribution in $[0,2\pi]$, the QCD background data distribution, and the signal (anomaly) scalar boson data distribution. (a) The expressibility (Expr) as a function of the different circuit architectures. (b) The entanglement capability $\langle \mathrm{Q} \rangle$ of the data encoding circuit as a function of the different circuit architectures. (c) The expressibility of the data encoding circuit as a function of the number of qubits ($n_q$). (d) The variance of the kernel $\mathrm{Var}_{z, z'}k(z,z')$ as a function of the number of qubits, where $k(z,z')$ is the kernel corresponding to the data encoding circuit , $z$ and $z'$ are data feature vectors sampled from the signal or background distributions.
• Figure 2: The quantum circuits. (a) Data encoding circuit $U(x)$, for a data point $x$, that implements the feature map of the unsupervised kernel machine and is used to define the quantum kernel $k(x_i,x_j) = \left|{\braket{0|U^\dagger(x_i) U(x_j)|0}}\right|^2$, where $G(\theta,\phi,\lambda)\in\text{SU(2)}$ is a universal 1-qubit gate, and $x_i$, for $i=0,1,\dots, n$, denotes the elements of the input feature vector $x$. The entanglement gates correspond to CNOT gates. (b) Quantum distance calculation circuit used to compute the similarity between an input sample and a cluster center in the QK-means algorithm. The prepared $\ket{\psi}$ and $\ket{\phi}$ states depend on the input feature vectors (Methods).
• Figure 2: The Autoencoder architecture. The model reduces the dimensionality of the high energy physics dataset from 300 dimensions per jet to latent space dimension $\ell$. The generated latent space serves as the input to the anomaly detection algorithms.
• Figure 3: Performance evaluation results. Each subplot displays the Receiver Operating Characteristic (ROC) curve and the corresponding Area Under the Curve (AUC) on test data for each model and each parameter of interest. Rows represent the model evaluation as a function of the parameters of interest: (a) new-physics anomalous signatures, (b) latent space dimension, and (c) the number of training samples. Columns correspond to the different anomaly detection models. A 5-fold testing is performed to assess the statistical significance of the results and of the differences in performance, using a test dataset of $10^5$ samples where half of the samples are anomalies and half are SM events. The best-performing classical model is a kernel model equipped with the Radial Basis Function (RBF) kernel. The uncertainty bands represent one standard deviation and are drawn only for the True Positive Rate (TPR) range of interest. For smaller values of TPR, the uncertainties increase due to low testing statistics and the bands are omitted for readability purposes.