[Paper Review] Unsupervised Event Classification with Graphs on Classical and Photonic Quantum Computers

Andrew Blance, Michael Spannowsky|arXiv (Cornell University)|Mar 5, 2021

Neural Networks and Reservoir ComputingComputer Science65 references38 citations

TL;DR

This paper proposes a novel unsupervised anomaly detection framework for high-energy physics using Gaussian Boson Sampling (GBS) on photonic quantum computers to embed event graphs into low-dimensional feature vectors, enabling efficient K-means and Q-means clustering. It demonstrates that GBS-based feature extraction outperforms classical eigenvalue methods, and Q-means achieves equivalent classification accuracy with O(log N) complexity versus classical O(N), enabling scalable, near-term quantum advantage at LHC trigger levels.

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.

Motivation & Objective

• To develop a data-driven anomaly detection method for New Physics searches at the LHC without prior assumptions about signal models.
• To leverage graph representations of high-energy collision events to encode both particle features and their relational structure.
• To explore the use of continuous-variable photonic quantum computers, specifically Gaussian Boson Sampling (GBS), for efficient feature embedding of event data.
• To implement and compare classical K-means and quantum-enhanced Q-means clustering for anomaly detection on graph-structured event data.
• To evaluate the scalability and performance benefits of quantum algorithms—particularly Q-means—on feature vectors of increasing dimensionality.

Proposed method

• Graphs are constructed from LHC events using particle constituents as nodes and their kinematic relationships (e.g., ∆R) as weighted edges.
• Classical feature vectors are generated via eigenvalue decomposition of the graph adjacency matrix as a baseline embedding method.
• GBS is used to generate quantum samples from the graph structure by encoding the adjacency matrix into a quantum circuit of squeezers and beamsplitters.
• GBS samples are processed to create low-dimensional feature vectors that preserve graph structure, replacing classical eigenvalue-based embeddings.
• K-means clustering is applied to both classical and GBS-generated feature vectors for anomaly detection.
• A quantum extension, Q-means, is implemented using the SwapTest to compute state overlaps, enabling logarithmic scaling with respect to feature vector length.

Experimental results

Research questions

• RQ1 Can Gaussian Boson Sampling effectively embed high-energy physics event graphs into low-dimensional feature vectors suitable for anomaly detection?
• RQ2 Does GBS-based feature extraction outperform classical eigenvalue-based methods in classifying rare signal events from Standard Model backgrounds?
• RQ3 Can Q-means clustering achieve equivalent classification performance to classical K-means while reducing time complexity from O(N) to O(log N) with respect to feature vector length?
• RQ4 Is the proposed quantum anomaly detection pipeline feasible for real-time implementation at the LHC trigger level using near-term photonic quantum hardware?
• RQ5 Can the continuous-variable quantum computing paradigm, particularly photonic GBS, provide a practical advantage over discrete qubit models for event classification in high-energy physics?

Key findings

• GBS-based feature extraction outperforms classical eigenvalue-based embedding in anomaly detection performance on a benchmark Higgs-portal signal search.
• The Q-means clustering algorithm achieves classification accuracy equivalent to classical K-means when applied to both classical and GBS-generated feature vectors.
• Q-means exhibits O(log N) time complexity with respect to feature vector length N, representing an exponential improvement over the classical O(N) scaling of K-means.
• The use of GBS enables rapid sampling—up to 100,000 samples per 100 ms—making it suitable for implementation at the LHC trigger level.
• The quantum circuit for Q-means, based on the SwapTest, is implementable on photonic hardware and maintains efficiency regardless of feature vector size.
• The method is scalable and compatible with continuous-variable quantum computing, suggesting potential for future integration with near-term photonic quantum devices.