Approximate Approximation on a Quantum Annealer

Many problems of industrial interest are NP-complete, and quickly exhaust resources of computational devices with increasing input sizes. Quantum annealers (QA) are physical devices that aim at this class of problems by exploiting quantum mechanical properties of nature. However, they compete with efficient heuristics and probabilistic or randomised algorithms on classical machines that allow for finding approximate solutions to large NP-complete problems. While first implementations of QA have become commercially available, their practical benefits are far from fully explored. To the best of our knowledge, approximation techniques have not yet received substantial attention. In this paper, we explore how problems' approximate versions of varying degree can be systematically constructed for quantum annealer programs, and how this influences result quality or the handling of larger problem instances on given set of qubits. We illustrate various approximation techniques on both, simulations and real QA hardware, on different seminal problems, and interpret the results to contribute towards a better understanding of the real-world power and limitations of current-state and future quantum computing.Comment: Proceedings of the 17th ACM International Conference on Computing Frontiers (CF 2020

Cornering Natural SUSY at LHC Run II and Beyond

We derive the latest constraints on various simplified models of natural SUSY with light higgsinos, stops and gluinos, using a detailed and comprehensive reinterpretation of the most recent 13 TeV ATLAS and CMS searches with $\sim 15$ fb$^{-1}$ of data. We discuss the implications of these constraints for fine-tuning of the electroweak scale. While the most "vanilla" version of SUSY (the MSSM with $R$-parity and flavor-degenerate sfermions) with 10% fine-tuning is ruled out by the current constraints, models with decoupled valence squarks or reduced missing energy can still be fully natural. However, in all of these models, the mediation scale must be extremely low ($<100$ TeV). We conclude by considering the prospects for the high-luminosity LHC era, where we expect the current limits on particle masses to improve by up to $\sim 1$ TeV, and discuss further model-building directions for natural SUSY that are motivated by this work.Comment: v2: added tree level- parton shower matching, fixed bug in Delphes, main results unchanged. 24 pages, 7 figures, plus appendi

Bayesian Surprise in Indoor Environments

This paper proposes a novel method to identify unexpected structures in 2D floor plans using the concept of Bayesian Surprise. Taking into account that a person's expectation is an important aspect of the perception of space, we exploit the theory of Bayesian Surprise to robustly model expectation and thus surprise in the context of building structures. We use Isovist Analysis, which is a popular space syntax technique, to turn qualitative object attributes into quantitative environmental information. Since isovists are location-specific patterns of visibility, a sequence of isovists describes the spatial perception during a movement along multiple points in space. We then use Bayesian Surprise in a feature space consisting of these isovist readings. To demonstrate the suitability of our approach, we take "snapshots" of an agent's local environment to provide a short list of images that characterize a traversed trajectory through a 2D indoor environment. Those fingerprints represent surprising regions of a tour, characterize the traversed map and enable indoor LBS to focus more on important regions. Given this idea, we propose to use "surprise" as a new dimension of context in indoor location-based services (LBS). Agents of LBS, such as mobile robots or non-player characters in computer games, may use the context surprise to focus more on important regions of a map for a better use or understanding of the floor plan.Comment: 10 pages, 16 figure

Holographic codes from hyperinvariant tensor networks

Holographic quantum-error correcting codes are models of bulk/boundary dualities such as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, where a higher-dimensional bulk geometry is associated with the code’s logical degrees of freedom. Previous discrete holographic codes based on tensor networks have reproduced the general code properties expected from continuum AdS/CFT, such as complementary recovery. However, the boundary states of such tensor networks typically do not exhibit the expected correlation functions of CFT boundary states. In this work, we show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions. This approach yields a dictionary between logical states in the bulk and the critical renormalization group flow of boundary states. Furthermore, these codes exhibit a state-dependent breakdown of complementary recovery as expected from AdS/CFT under small quantum gravity corrections

Holographic Codes from Hyperinvariant Tensor Networks

Holographic quantum-error correcting codes are models of bulk/boundary dualities such as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, where a higher-dimensional bulk geometry is associated with the code's logical degrees of freedom. Previous discrete holographic codes based on tensor networks have reproduced the general code properties expected from continuum AdS/CFT, such as complementary recovery. However, the boundary states of such tensor networks typically do not exhibit the expected correlation functions of CFT boundary states. In this work, we show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions. This approach yields a dictionary between logical states in the bulk and the critical renormalization group flow of boundary states. Furthermore, these codes exhibit a state-dependent breakdown of complementary recovery as expected from AdS/CFT under small quantum gravity corrections.Comment: 10 pages, 7 figure

Alternative Routen in komplexen Umgebungen

Durch die immense Verbreitung kostengünstiger GPS-Empfänger, eingebaut in mobile Endgeräte, wurde in den letzten Jahren eine beeindruckend starke Nutzung von ortsbezogenen Anwendungen und Diensten erreicht. Ein beliebter Anwendungsfall ist die Navigation im Straßenverkehr zusammen mit der Präsentation von alternativen Routen, die dem Anwender eine Auswahl nach eigenen Präferenzen oder Erfahrungen ermöglicht. Die Wegefindung in komplexen Umgebungen unterscheidet sich von der in Straßennetzen hauptsächlich durch die Tatsache, dass sich ein Anwender nahezu in alle Richtungen bewegen kann. Beispiele hierfür sind Fußgänger in Flughäfen, Krankenhäusern, Messehallen oder Parks, mobile Roboter in Industrieanlagen oder Lagerhallen, sowie Nicht-Spieler-Charaktere in Computerspielen. Auch in diesen Szenarien ist das Vorhalten von alternativen Routen sinnvoll, um beispielsweise eine personalisierte Navigation zu ermöglichen, proaktiv Stau zu vermeiden oder taktische Bewegungen durchzuführen. In der vorliegenden Arbeit werden Ansätze und Verfahren vorgestellt, die das Thema der alternativen Routen in komplexen Umgebungen auf unterschiedlichen thematischen Ebenen behandelt. Darunter fallen die Berechnung alternativer Routen in Freiflächen, der Vergleich geospatialer Trajektorien, sowie die Identifizierung von Strukturen in Gebäuden. Im ersten Teil der Arbeit werden alternative Routen in komplexen Umgebungen mittels des topologischen Konzepts der Homotopie definiert, sodass zwei Routen als Alternativen zueinander angesehen werden, wenn sie Hindernisse unterschiedlich umlaufen. Hierzu wird eine effiziente Annäherung des Tests auf Homotopie vorgestellt und es werden zwei Algorithmen zum Berechnen solcher Routen implementiert. Anschließend findet eine strukturierte Darstellung bestehender Qualitätsmetriken für alternative Routen und Alternativgraphen in Straßennetzen statt, woraufhin die Übertragbarkeit dieser Ansätze auf komplexe Umgebungen diskutiert wird. Im zweiten Teil der Arbeit werden Ansätze zum direkten Vergleich von Routen vorgestellt. Einerseits wird ein Scoring von Routen basierend auf der Annahme vorgeschlagen, dass Routen, die oft auf einem kürzesten Pfad liegen, auch oft durchlaufen werden. Andererseits wird ein System vorgestellt, das die Berechnung archetypischer Routen ermöglicht, indem es aus einer Menge von Routen die extremsten Exemplare extrahiert. Korrespondierend dazu wird die archetypische Distanz definiert, mit der Routen nicht nur geometrisch, sondern in einem mehrdimensionalen Merkmalsraum verglichen werden können. Schließlich wird im dritten Teil der Arbeit die quantitative Analyse der visuellen Wahrnehmung von Raum in den Kontext alternativer Routen integriert. Basierend auf der Idee sogenannter Isovisten wird die lokale Umgebung eines Anwenders angenähert, um somit alternative Routen zu berechnen, diese zu annotieren, und schließlich Strukturen in Gebäuden zu ermitteln. Zusammengefasst können die Beiträge der vorliegenden Arbeit in ihrer Gesamtheit als ein Werkzeugkasten verstanden werden, der von weiteren ortsbezogenen Anwendungen und Diensten verwendet werden kann.Due to the immense dissemination of low-cost GPS receivers built into mobile devices, an impressive use of location-based services has been achieved in recent years. A popular application is navigation in road networks in conjunction with the presentation of alternative routes that allows users a choice according to their own preferences or experiences. Route finding in complex environments differs from that in road networks mainly due to the fact that a user can move almost in all directions. Examples include pedestrians in airports, hospitals, exhibition halls, or parks, mobile robots in industrial facilities or warehouses, as well as non-player characters in computer games. In these scenarios the provision of alternative routes is useful, too, for example, to enable personalized navigation, to avoid jams proactively, or to carry out tactical movements. This thesis presents approaches which deal with the topic of alternative routes in complex environments at different thematic levels. This includes the calculation of alternative routes in open space, the comparison of geospatial trajectories, and the identification of structures in buildings. First, alternative routes in complex environments are defined using the topological concept of homotopy, so that two routes can be considered alternative if they pass obstacles differently. For this purpose an efficient approximation of the homotopy test is presented together with the implementation of two algorithms for the calculation of such routes. Subsequently a structured presentation of existing quality metrics for alternative routes and alternative graphs in road networks takes place, whereupon the transferability of these approaches into complex environments is discussed. Second, approaches for the direct comparison of routes are presented. On the one hand, a scoring of routes is suggested based on the assumption that routes, which often lie on a shortest paths, are also often traversed. On the other hand, a system is presented that allows the calculation of archetypal routes by extracting the most extreme instances from a set of routes. Corresponding to this, the archetypal distance is defined, with which routes can be compared not only geometrically but in a multi-dimensional feature space. Third, the quantitative analysis of the visual perception of space is incorporated into the context of alternative routes. Based on the idea of so-called Isovists, a user's local environment is approximated in order to calculate alternative routes, to annotate them, and to determine structures in buildings. In summary, the contributions of this thesis can be understood in their entirety as a toolbox which can be used by other location-based services

Influence of Different 3SAT-to-QUBO Transformations on the Solution Quality of Quantum Annealing: A Benchmark Study

To solve 3SAT instances on quantum annealers they need to be transformed to an instance of Quadratic Unconstrained Binary Optimization (QUBO). When there are multiple transformations available, the question arises whether different transformations lead to differences in the obtained solution quality. Thus, in this paper we conduct an empirical benchmark study, in which we compare four structurally different QUBO transformations for the 3SAT problem with regards to the solution quality on D-Wave's Advantage_system4.1. We show that the choice of QUBO transformation can significantly impact the number of correct solutions the quantum annealer returns. Furthermore, we show that the size of a QUBO instance (i.e., the dimension of the QUBO matrix) is not a sufficient predictor for solution quality, as larger QUBO instances may produce better results than smaller QUBO instances for the same problem. We also empirically show that the number of different quadratic values of a QUBO instance, combined with their range, can significantly impact the solution quality

Approximative lookup-tables and arbitrary function rotations for facilitating NISQ-implementations of the HHL and beyond

Many promising applications of quantum computing with a provable speedup center around the HHL algorithm. Due to restrictions on the hardware and its significant demand on qubits and gates in known implementations, its execution is prohibitive on near-term quantum computers. Aiming to facilitate such NISQ-implementations, we propose a novel circuit approximation technique that enhances the arithmetic subroutines in the HHL, which resemble a particularly resource-demanding component in small-scale settings. For this, we provide a description of the algorithmic implementation of space-efficient rotations of polynomial functions that do not demand explicit arithmetic calculations inside the quantum circuit. We show how these types of circuits can be reduced in depth by providing a simple and powerful approximation technique. Moreover, we provide an algorithm that converts lookup-tables for arbitrary function rotations into a structure that allows an application of the approximation technique. This allows implementing approximate rotation circuits for many polynomial and non-polynomial functions. Experimental results obtained for realistic early-application dimensions show significant improvements compared to the state-of-the-art, yielding small circuits while achieving good approximations