Unsupervised Event Classification with Graphs on Classical and Photonic Quantum Computers

Abstract

Photonic Quantum Computers provides several benefits over the discrete qubit-based paradigm of quantum computing. By using the power of continuous-variable computing we build an anomaly detection model to use on searches for New Physics. Our model uses Gaussian Boson Sampling, a $\#$P-hard problem and thus not efficiently accessible to classical devices. This is used to create feature vectors from graph data, a natural format for representing data of high-energy collision events. A simple K-means clustering algorithm is used to provide a baseline method of classification. We then present a novel method of anomaly detection, combining the use of Gaussian Boson Sampling and a quantum extension to K-means known as Q-means. This is found to give equivalent results compared to the classical clustering version while also reducing the $\mathcal{O}$ complexity, with respect to the sample's feature-vector length, from $\mathcal{O}(N)$ to $\mathcal{O}(\mbox{log}(N))$. Due to the speed of the sampling algorithm and the feasibility of near-term photonic quantum devices, anomaly detection at the trigger level can become practical in future LHC runs.