Vasilis Belis

Vasilis Belis, Kinga Anna Woźniak, Ema Puljak et al.

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.

Julian Schuhmacher, Laura Boggia, Vasilis Belis et al.

Much hope for finding new physics phenomena at microscopic scale relies on the observations obtained from High Energy Physics experiments, like the ones performed at the Large Hadron Collider (LHC). However, current experiments do not indicate clear signs of new physics that could guide the development of additional Beyond Standard Model (BSM) theories. Identifying signatures of new physics out of the enormous amount of data produced at the LHC falls into the class of anomaly detection and constitutes one of the greatest computational challenges. In this article, we propose a novel strategy to perform anomaly detection in a supervised learning setting, based on the artificial creation of anomalies through a random process. For the resulting supervised learning problem, we successfully apply classical and quantum Support Vector Classifiers (CSVC and QSVC respectively) to identify the artificial anomalies among the SM events. Even more promising, we find that employing an SVC trained to identify the artificial anomalies, it is possible to identify realistic BSM events with high accuracy. In parallel, we also explore the potential of quantum algorithms for improving the classification accuracy and provide plausible conditions for the best exploitation of this novel computational paradigm.

Patrick Odagiu, Vasilis Belis, Lennart Schulze et al.

Data sets that are specified by a large number of features are currently outside the area of applicability for quantum machine learning algorithms. An immediate solution to this impasse is the application of dimensionality reduction methods before passing the data to the quantum algorithm. We investigate six conventional feature extraction algorithms and five autoencoder-based dimensionality reduction models to a particle physics data set with 67 features. The reduced representations generated by these models are then used to train a quantum support vector machine for solving a binary classification problem: whether a Higgs boson is produced in proton collisions at the LHC. We show that the autoencoder methods learn a better lower-dimensional representation of the data, with the method we design, the Sinkclass autoencoder, performing 40% better than the baseline. The methods developed here open up the applicability of quantum machine learning to a larger array of data sets. Moreover, we provide a recipe for effective dimensionality reduction in this context.

Vasilis Belis, Joseph Bowles, Rishabh Gupta et al.

This article presents an argument for why quantum computers could unlock new methods for machine learning. We argue that spectral methods, in particular those that learn, regularise, or otherwise manipulate the Fourier spectrum of a machine learning model, are often natural for quantum computers. For example, if a generative machine learning model is represented by a quantum state, the Quantum Fourier Transform allows us to manipulate the Fourier spectrum of the state using the entire toolbox of quantum routines, an operation that is usually prohibitive for classical models. At the same time, spectral methods are surprisingly fundamental to machine learning: A spectral bias has recently been hypothesised to be the core principle behind the success of deep learning; support vector machines have been known for decades to regularise in Fourier space, and convolutional neural nets build filters in the Fourier space of images. Could, then, quantum computing open fundamentally different, much more direct and resource-efficient ways to design the spectral properties of a model? We discuss this potential in detail here, hoping to stimulate a direction in quantum machine learning research that puts the question of ``why quantum?'' first.

Vasilis Belis, Giulio Crognaletti, Matteo Argenton et al.

Quantum computers provide a super-exponential speedup for performing a Fourier transform over the symmetric group, an ability for which practical use cases have remained elusive so far. In this work, we leverage this ability to unlock spectral methods for machine learning over permutation-structured data, which appear in applications such as multi-object tracking and recommendation systems. It has been shown previously that a powerful way of building probabilistic models over permutations is to use the framework of non-Abelian harmonic analysis, as the model's group Fourier spectrum captures the interaction complexity: "low frequencies" correspond to low order correlations, and "high frequencies" to more complex ones. This can be used to construct a Markov chain model driven by alternating steps of diffusion (a group-equivariant convolution) and conditioning (a Bayesian update). However, this approach is computationally challenging and hence limited to simple approximations. Here we construct a quantum algorithm that encodes the exact probabilistic model -- a classically intractable object -- into the amplitudes of a quantum state by making use of the Quantum Fourier Transform (QFT) over the symmetric group. We discuss the scaling, limitations, and practical use of such an approach, which we envision to be a first step towards useful applications of non-Abelian QFTs.

Till Muser, Elias Zapusek, Vasilis Belis et al.

There is an ongoing effort to find quantum speedups for learning problems. Recently, [Y. Liu et al., Nat. Phys. $\textbf{17}$, 1013--1017 (2021)] have proven an exponential speedup for quantum support vector machines by leveraging the speedup of Shor's algorithm. We expand upon this result and identify a speedup utilizing Grover's algorithm in the kernel of a support vector machine. To show the practicality of the kernel structure we apply it to a problem related to pattern matching, providing a practical yet provable advantage. Moreover, we show that combining quantum computation in a preprocessing step with classical methods for classification further improves classifier performance.

Vasilis Belis, Patrick Odagiu, Thea Klæboe Årrestad

The detection of out-of-distribution data points is a common task in particle physics. It is used for monitoring complex particle detectors or for identifying rare and unexpected events that may be indicative of new phenomena or physics beyond the Standard Model. Recent advances in Machine Learning for anomaly detection have encouraged the utilization of such techniques on particle physics problems. This review article provides an overview of the state-of-the-art techniques for anomaly detection in particle physics using machine learning. We discuss the challenges associated with anomaly detection in large and complex data sets, such as those produced by high-energy particle colliders, and highlight some of the successful applications of anomaly detection in particle physics experiments.

Vasilis Belis, Patrick Odagiu, Michele Grossi et al.

Quantum machine learning provides a fundamentally different approach to analyzing data. However, many interesting datasets are too complex for currently available quantum computers. Present quantum machine learning applications usually diminish this complexity by reducing the dimensionality of the data, e.g., via auto-encoders, before passing it through the quantum models. Here, we design a classical-quantum paradigm that unifies the dimensionality reduction task with a quantum classification model into a single architecture: the guided quantum compression model. We exemplify how this architecture outperforms conventional quantum machine learning approaches on a challenging binary classification problem: identifying the Higgs boson in proton-proton collisions at the LHC. Furthermore, the guided quantum compression model shows better performance compared to the deep learning benchmark when using solely the kinematic variables in our dataset.

Mikel Casals, Vasilis Belis, Elias F. Combarro et al.

Graph Neural Networks (GNNs) are effective for processing graph-structured data but face challenges with large graphs due to high memory requirements and inefficient sparse matrix operations on GPUs. Quantum Computing (QC) offers a promising avenue to address these issues and inspires new algorithmic approaches. In particular, Quantum Graph Neural Networks (QGNNs) have been explored in recent literature. However, current quantum hardware limits the dimension of the data that can be effectively encoded. Existing approaches either simplify datasets manually or use artificial graph datasets. This work introduces the Guided Graph Compression (GGC) framework, which uses a graph autoencoder to reduce both the number of nodes and the dimensionality of node features. The compression is guided to enhance the performance of a downstream classification task, which can be applied either with a quantum or a classical classifier. The framework is evaluated on the Jet Tagging task, a classification problem of fundamental importance in high energy physics that involves distinguishing particle jets initiated by quarks from those by gluons. The GGC is compared against using the autoencoder as a standalone preprocessing step and against a baseline classical GNN classifier. Our numerical results demonstrate that GGC outperforms both alternatives, while also facilitating the testing of novel QGNN ansatzes on realistic datasets.