Modeling routing problems in QUBO with application to ride-hailing

Many emerging commercial services are based on the sharing or pooling of resources for common use with the aim of reducing costs. Businesses such as delivery-, mobility-, or transport-as-a-service have become standard in many parts of the world, fulfilling on-demand requests for customers in live settings. However, it is known that many of these problems are NP-hard, and therefore both modeling and solving them accurately is a challenge. Here we focus on one such routing problem, the Ride Pooling Problem (RPP), where multiple customers can request on-demand pickups and drop-offs from shared vehicles within a fleet. The combinatorial optimization task is to optimally pool customer requests using the limited set of vehicles, akin to a small-scale flexible bus route. In this work, we propose a quadratic unconstrained binary optimization (QUBO) program and introduce efficient formulation methods for the RPP to be solved using metaheuristics, and specifically emerging quantum optimization algorithms

Equivariant quantum circuits for learning on weighted graphs

Variational quantum algorithms are the leading candidate for advantage on near-term quantum hardware. When training a parametrized quantum circuit in this setting to solve a specific problem, the choice of ansatz is one of the most important factors that determines the trainability and performance of the algorithm. In quantum machine learning (QML), however, the literature on ansatzes that are motivated by the training data structure is scarce. In this work, we introduce an ansatz for learning tasks on weighted graphs that respects an important graph symmetry, namely equivariance under node permutations. We evaluate the performance of this ansatz on a complex learning task, namely neural combinatorial optimization, where a machine learning model is used to learn a heuristic for a combinatorial optimization problem. We analytically and numerically study the performance of our model, and our results strengthen the notion that symmetry-preserving ansatzes are a key to success in QML.Comment: 17+3 pages, 10 figures, version accepted at journa

Quantum Computing Techniques for Multi-Knapsack Problems

Optimization problems are ubiquitous in various industrial settings, and multi-knapsack optimization is one recurrent task faced daily by several industries. The advent of quantum computing has opened a new paradigm for computationally intensive tasks, with promises of delivering better and faster solutions for specific classes of problems. This work presents a comprehensive study of quantum computing approaches for multi-knapsack problems, by investigating some of the most prominent and state-of-the-art quantum algorithms using different quantum software and hardware tools. The performance of the quantum approaches is compared for varying hyperparameters. We consider several gate-based quantum algorithms, such as QAOA and VQE, as well as quantum annealing, and present an exhaustive study of the solutions and the estimation of runtimes. Additionally, we analyze the impact of warm-starting QAOA to understand the reasons for the better performance of this approach. We discuss the implications of our results in view of utilizing quantum optimization for industrial applications in the future. In addition to the high demand for better quantum hardware, our results also emphasize the necessity of more and better quantum optimization algorithms, especially for multi-knapsack problems.Comment: 20 page

New physics searches in angular shapes of photon+jet events in 2013 ATLAS data

The Large Hadron Collider at CERN, Switzerland, was built to both refine current Standard Model measurements, as well as discover new physics beyond the Standard Model. Using data from the general-purpose ATLAS detector, we take a step towards answering one of these questions: are quarks point-like, or do they themselves have sub-structure? By investigating the angular correlations in photon+jet events we address this question. The final goal of this thesis was to produce a feasible method to test deviations from the Standard Model using 2012 ATLAS data. A new data-driven background estimation analysis technique was developed to test for significant deviations from Standard Model predictions. We parametrize the angular separation between the leading photon and jet in each event with the variable $\psi = \log(\exp(|\eta_\gamma-\eta_j|)+1)$ (where $\eta$ is pseudorapidity) using standard ATLAS Monte Carlo generators Pythia, Sherpa, and JetPhox. Kinematic comparisons are performed between 2012 ATLAS data and Monte Carlo samples to show how well data is described by the generators. We take the ratio of the number of narrowly-separated ($\psi < 1.5$) to selected events with $\psi < 5$ as a function of invariant mass of the final state photon and the final state jet, resulting in our observable distribution $F_\psi$. We fit the numerator and denominator invariant mass distributions separately and obtain the background estimate of the $F_\psi$ distribution in each bin by dividing the results of the fit in each bin. We use a bootstrap method for statistical error estimation. Our analysis techniques were optimized with the Excited Quark model as a benchmark model. Using the developed methodology for background estimation, we proceed to estimate the expected signal sensitivity of this analysis technique to excited quark production in the full 2012 ATLAS dataset of 20.3 fb$^{-1}$.Le Grand collisionneur de hadrons au CERN, en Suisse, a été construit afin d'améliorer les mesures actuelles du Modèle Standard et pour tenter de découvrir des phénomènes physiques qui ne sont pas décrits par le Modèle Standard. En utilisant les données amassées par le détecteur ATLAS, nous nous penchons sur un de ces phénomènes: les quarks sont-ils des particules ponctuelles ou ont-ils plutôt une structure interne? Nous nous servons des corrélations angulaires entre les photons et les gerbes de particules dans l'état final de collisions à hautes énergies pour étudier la question. Le but de ce mémoire est de démontrer l'efficacité de cette technique d'analyse et d'en étudier la performance avec les données prises par ATLAS en 2012. Nous présentons une nouvelle technique d'estimation du bruit de fond causé par les processus physiques du Modèle Standard et un test qui permet de déterminer si les données d'ATLAS dévient significativement par rapport à ce bruit de fond. Nous paramétrons la séparation angulaire entre le photon le plus énergétique et la gerbe la plus énergétique dans chaque événement par $\psi = \log(\exp(|\eta_\gamma-\eta_j|)+1)$ (où $\eta$ est la pseudorapidité) en utilisant des données simulées par les générateurs Monte Carlo Pythia, Sherpa et JetPhox. Nous comparons les distributions des variables cinétiques entre les données ATLAS et les événement simulés pour démontrer que les données simulées reproduisent bien les caractéristiques des données réelles. Nous définissons un nouvel observable $F_\psi$ qui représente la fraction des événements qui ont une petite séparation angulaire ( $\psi$ est plus petit que 1.5) parmi les événements acceptés ( $\psi$ est plus petit que 5) en fonction de la masse au repos du système photon+gerbe. Un ajustement de courbe est fait séparément pour les distributions de masse au repos qui constituent le numérateur et le dénominateur de l'observable $F_\psi$. La prédiction du bruit de fond en $F_\psi$ dans chaque intervalle de masse au repos est obtenue par le résultat de la division des valeurs des deux courbes ajustées dans cet intervalle. L'incertitude statistique est calculée à l'aide d'une méthode de type "bootstrap". La méthode analytique est optimisée en utilisant comme modèle de référence le modèle du quark excité. Avec notre nouvelle méthode d'estimation du bruit de fond, notre technique d'analyse et notre signal de référence, nous mesurons la valeur attendee pour la détection d'un signal de quark excité dans les 20.3 fb^-1 de données ATLAS de 2012

Quantum Annealing for Industry Applications: Introduction and Review

Quantum annealing is a heuristic quantum optimization algorithm that can be used to solve combinatorial optimization problems. In recent years, advances in quantum technologies have enabled the development of small- and intermediate-scale quantum processors that implement the quantum annealing algorithm for programmable use. Specifically, quantum annealing processors produced by D-Wave Systems have been studied and tested extensively in both research and industrial settings across different disciplines. In this paper we provide a literature review of the theoretical motivations for quantum annealing as a heuristic quantum optimization algorithm, the software and hardware that is required to use such quantum processors, and the state-of-the-art applications and proofs-of-concepts that have been demonstrated using them. The goal of our review is to provide a centralized and condensed source regarding applications of quantum annealing technology. We identify the advantages, limitations, and potential of quantum annealing for both researchers and practitioners from various fields.Comment: major revision with extended noise section and discussion of alternative platform

Traffic Flow Optimization Using a Quantum Annealer

Quantum annealing algorithms belong to the class of meta-heuristic tools, applicable for solving binary optimization problems. Hardware implementations of quantum annealing, such as the quantum processing units (QPUs) produced by D-Wave Systems, have been subject to multiple analyses in research, with the aim of characterizing the technology's usefulness for optimization and sampling tasks. In this paper, we present a real-world application that uses quantum technologies. Specifically, we show how to map certain parts of the real-world traffic flow optimization problem to be suitable for quantum annealing. We show that time-critical optimization tasks, such as continuous redistribution of position data for cars in dense road networks, are suitable candidates for quantum applications. Due to the limited size and connectivity of current-generation D-Wave QPUs, we use a hybrid quantum and classical approach to solve the traffic flow problem.Comment: 17 pages, 6 figure