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arXiv:2103.03897 · Journal of High Energy Physics

Unsupervised event classification with graphs on classical and photonic quantum computers

Andrew Blance, Michael Spannowsky

Published Aug 31, 2021• 39 citations
arXivHTMLPDF

Abstract

Abstract Photonic Quantum Computers provide 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 $$ \mathcal{O} $$ O complexity, with respect to the sample’s feature-vector length, from $$ \mathcal{O}(N) $$ O N to $$ \mathcal{O}\left(\log (N)\right) $$ O log N .

DOI
10.1007/jhep08(2021)170

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Abstract Photonic Quantum Computers provide 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 O\mathcal{O}O O complexity, with respect to the sample’s feature-vector length, from O(N)\mathcal{O}(N)O(N) O N to O(log⁡(N))\mathcal{O}\left(\log (N)\right)O(log(N)) O log N .
Gaussian Boson Sampling (GBS) generates random samples of photon-click patterns from a class of probability distributions that are hard for a classical computer to sample from. Despite heroic demonstrations of quantum supremacy using GBS, Boson Sampling, and instantaneous quantum polynomial (IQP) algorithms, systematic evaluations of the power of these quantum-enhanced random samplers when applied to provably hard problems, and performance comparisons with best-known classical algorithms have been lacking. We propose a hybrid quantum-classical algorithm using the GBS for the NP-complete problem of determining if two graphs are a vertex minor of one another. The graphs are encoded in GBS and the generated random samples serve as feature vectors in a support vector machine (SVM) classifier. We find a graph embedding that allows trading between the one-shot classification accuracy and the amount of input squeezing, a hard-to-produce quantum resource, followed by repeated trials and a majority vote to reach an overall desired accuracy. We introduce a new classical algorithm based on graph spectra, which we show outperforms various well-known graph-similarity algorithms. We compare the performance of our algorithm with this classical algorithm and analyze their time versus problem-size scaling, to yield a desired classification accuracy. Our simulation results suggest that with a near-term realizable GBS device—5 dB pulsed squeezers, 12-mode unitary, and reasonable assumptions on coupling efficiency, on-chip losses, and detection efficiency of photon number resolving detectors—we can solve 12-node vertex-minor instances with about 103fold lower time compared to a powerful desktop computer.
We present a variation of a quantum algorithm for the machine learning task of classification with graph-structured data. The algorithm implements a feature extraction strategy that is based on Gaussian boson sampling (GBS), a near-term model of quantum computing. However, unlike the currently proposed algorithms for this problem, our GBS setup requires only binary (light or no light) detectors, as opposed to photon-number-resolving detectors. Binary detectors are technologically simpler and can operate near room temperature, making our algorithm much less complex and costly to implement physically. We also investigate the connection between graph theory and the Torontonian matrix function which characterizes the probabilities of binary GBS detection events.
Photonics chips on which one can perform Gaussian Boson Sampling have become accessible on the cloud, in particular the X8 chip of Xanadu. In this technical report, we study its potential use as a first step towards graph classification on quantum devices. In order to achieve this goal, we study the generated samples of the graph embedding method which leads to feature vectors. This is done on a restricted class of unweighted, undirected and loop-free graphs. Hardware constraints are matched to properties of graphs that can be encoded. We report experiments on the X8 chip as well as comparisons to numerical simulations on a classical computer and analytical solutions. We conclude this technical report by trying to take photon loss into account and explain the observed results accordingly.
Abstract Gaussian Boson Sampling (GBS) is a non-universal model for quantum computing inspired by the original formulation of the Boson Sampling (BS) problem. Nowadays, it represents a paradigmatic quantum platform to reach the quantum advantage regime in a specific computational model. Indeed, thanks to the implementation in photonics-based processors, the latest GBS experiments have reached a level of complexity where the quantum apparatus has solved the task faster than currently up-to-date classical strategies. In addition, recent studies have identified possible applications beyond the inherent sampling task. In particular, a direct connection between photon counting of a genuine GBS device and the number of perfect matchings in a graph has been established. In this work, we propose to exploit such a connection to benchmark GBS experiments. We interpret the properties of the feature vectors of the graph encoded in the device as a signature of correct sampling from the true input state. Within this framework, two approaches are presented. The first method exploits the distributions of graph feature vectors and classification via neural networks. The second approach investigates the distributions of graph kernels. Our results provide a novel approach to the actual need for tailored algorithms to benchmark large-scale Gaussian Boson Samplers.
The standard model (SM) of particle physics represents a theoretical paradigm for the description of the fundamental forces of nature. Despite its broad applicability, the SM does not enable the description of all physically possible events. The detection of events that cannot be described by the SM, which are typically referred to as anomalous, and the related potential discovery of exotic physical phenomena is a non-trivial task. The challenge becomes even greater with next-generation colliders that will produce even more events with additional levels of complexity. The additional data complexity motivates the search for unsupervised anomaly detection methods that do not require prior knowledge about the underlying models. In this work, we develop such a technique. More explicitly, we employ a quantum generative adversarial network to identify anomalous events. The method learns the background distribution from SM data and, then, determines whether a given event is characteristic for the learned background distribution. The proposed quantum-powered anomaly detection strategy is tested on proof-of-principle examples using numerical simulations and IBM Quantum processors. We find that the quantum generative techniques using ten times fewer training data samples can yield comparable accuracy to the classical counterpart for the detection of the Graviton and Higgs particles. Additionally, we empirically compute the capacity of the quantum model and observe an improved expressivity compared to its classical counterpart.
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. The ongoing quest in particle physics to discover fundamentally new phenomena necessitates the continuous development of algorithms and technologies. The authors propose a methodology based on quantum machine learning that can identify new phenomena in proton collision experiments, showing that it can outperform its classical counterparts when sufficient quantum computing resources are utilized.