• Background: QCD di-jet events • Anomalous signatures: - Narrow and Broad RS gravitons ( ) - New scalar boson ( ) G →W W A →HZ →Z Z Z Quantum anomaly detection in the latent space of proton collision events at the LHC V.Belis1,2, Ema Puljak1,3, K.A.Woźniak1,4, G.Dissertori2, F.Reiter2, M.Grossi1, M.Pierini1, P.Barkoutsos5, I.Tavernelli5, S.Vallecorsa1 We propose a new strategy for anomaly detection at the LHC based on unsupervised quantum machine learning algorithms. To accommodate the constraints on the problem size dictated by the limitations of current quantum hardware we develop a classical convolutional autoencoder. The designed quantum anomaly detection models, namely an unsupervised kernel machine and two clustering algorithms, are trained to find new-physics events in the latent representation of LHC data produced by the autoencoder. The performance of the quantum algorithms is benchmarked against classical counterparts on different new-physics scenarios and its dependence on the dimensionality of the latent space and the size of the training dataset is studied. For kernel-based anomaly detection, we identify a regime where the quantum model significantly outperforms its classical counterpart. An instance of the kernel machine is implemented on a quantum computer to verify its suitability for available hardware. We demonstrate that the observed consistent performance advantage is related to the inherent quantum properties of the circuit used. Abstract LHC pp collision (MC simulation) Physics signatures Features (Δη, Δϕ, pT) 100 particles x ... ... ... ... ... ... ℓ Dimensionality reduction Models for Quantum anomaly detection • To address limitations of NISQ devices • Convolutional AE - acts per-particle level Quantum Kernel: k(xi, xj) = |⟨0|U†(xi)U(xj)|0⟩|2 Unsupervised quantum kernel machine Designed data encoding map to be hardware efficient, adequately expressive and have non-trivial interaction between input features U(x) G (θ, ϕ, λ) ∈SU(2) data encoding c o s ( θ 2 ) e−iλ s i n ( θ 2 ) eiϕ s i n ( θ 2 ) ei(ϕ+λ)s i n ( θ 2 ) Clustering algorithms Use amplitude encoding to map inputs to quantum states Cluster assignment using quantum circuits for distance calculation and optimization procedures QK-means / QK-medians QK-means quantum circuit 1. Distance calculation (Figure below/ H gate on MSQ - destructive interference probabilities) 2. Grover search algorithm / Hybrid quantum-classical optimization Results Convolutional AE Conclusions • We presented a systematic study of QML models for anomaly detection in proton collisions, comparing them as a function of anomalous physics signatures, latent dimensionality and training size • We observed the window of quantum advantage for unsupervised quantum kernel machine • Quantum clustering algorithms show advantage for smaller training size • Preprint: arXiv:2301.10780 Quantum harware results Kernel Machine Run AUC htr⇢2i Hardware L = 1 0.844 0.271(6) Ideal L = 1 0.999 1 Hardware L = 3 0.997 0.15(2) Ideal L = 3 1.0 1 Classical 0.998 - L = number of repetitions of U(x) Quantum advantage window • Consistent performance advantage ( > 1) in parameter space () • Inscrease of expressibility and entanglement of circuit leads to rise of performance up to maximum L=4 (left figure) • For L=3 algorithm performs better for higher number of qubits (inner plot in left figure) ΔQC 1 2 3 4 5