277 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Analog Photonics Computing for Information Processing, Inference and Optimisation
This review presents an overview of the current state-of-the-art in photonics
computing, which leverages photons, photons coupled with matter, and
optics-related technologies for effective and efficient computational purposes.
It covers the history and development of photonics computing and modern
analogue computing platforms and architectures, focusing on optimization tasks
and neural network implementations. The authors examine special-purpose
optimizers, mathematical descriptions of photonics optimizers, and their
various interconnections. Disparate applications are discussed, including
direct encoding, logistics, finance, phase retrieval, machine learning, neural
networks, probabilistic graphical models, and image processing, among many
others. The main directions of technological advancement and associated
challenges in photonics computing are explored, along with an assessment of its
efficiency. Finally, the paper discusses prospects and the field of optical
quantum computing, providing insights into the potential applications of this
technology.Comment: Invited submission by Journal of Advanced Quantum Technologies;
accepted version 5/06/202
Quantum Computing for Airline Planning and Operations
Classical algorithms and mathematical optimization techniques have beenused extensively by airlines to optimize their profit and ensure that regulationsare followed. In this thesis, we explore which role quantum algorithmscan have for airlines. Specifically, we have considered the two quantum optimizationalgorithms; the Quantum Approximate Optimization Algorithm(QAOA) and Quantum Annealing (QA). We present a heuristic that integratesthese quantum algorithms into the existing classical algorithm, whichis currently employed to solve airline planning problems in a state-of-the-artcommercial solver. We perform numerical simulations of QAOA circuits andfind that linear and quadratic algorithm depth in the input size can be requiredto obtain a one-shot success probability of 0.5. Unfortunately, we areunable to find performance guarantees. Finally, we perform experiments withD-waveâs newly released QA machine and find that it outperforms 2000Q formost instances
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Exploring many-body Physics with Recurrent Neural Networks
Originally developed within the natural language processing community, Recurrent neural networks (RNNs) have enabled remarkable progress in speech recognition and machine translation. These architectures belong to the class of autoregressive generative models which allow for exact likelihood estimation and for a perfect sampling of multi-modal complex probability distributions. These desirable features suggest that RNNs may serve as ansatzes wave functions in the context of Variational Monte Carlo (VMC), where ansatzes based on a Markov chain Monte Carlo sampling scheme can be limited by long autocorrelation time. The main vision developed here replaces words with physical degrees of freedom as inputs to the RNN in order to transfer this technology to the context of many-body physics. In this thesis, we develop RNN wave functions in multiple spatial dimensions and with different flavors and symmetry considerations that can suit the need for different variational calculations. We demonstrate the power of RNN wave functions on various prototypical systems in one, two, and three spatial dimensions. We show that our ansatz can compete and outperform state-of-the-art methods such as Density Matrix Renormalization Group (DMRG). We also illustrate how to estimate observables, and entanglement, with which we can study different phases of matter including conventional and topologically ordered states, as well as phase transitions among different phases. We also develop a scheme for simulating a variational version of classical and quantum annealing for the purpose of solving combinatorial optimization problems. We demonstrate that our scheme, tested on various RNNs architectures, shows superior average performances compared to Markov-chain Monte Carlo implementation of classical annealing and quantum annealing on prototypical and real-world combinatorial optimization problems. We also highlight the importance of the annealing scheme in overcoming local minima in a traditional VMC optimization, especially in frustrated systems. We conclude this thesis with examples of exact constructions of traditional probability distributions based on RNNs as a first step toward understanding the promising performances of these architectures. In addition to tensor network and Monte Carlo methods, we believe that RNNs are a valuable toolbox for physicists to help address open questions in classical and quantum many-body physics
Larger matchings and independent sets in regular uniform hypergraphs of high girth
In this note we analyze two algorithms, one for producing a matching and one
for an independent set, on -uniform -regular hypergraphs of large girth.
As a result we obtain new lower bounds on the size of a maximum matching or
independent set in such hypergraphs
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum
Angles and devices for quantum approximate optimization
A potential application of emerging Noisy Intermediate-Scale Quantum (NISQ) devices is that of approximately solving combinatorial optimization problems. This thesis investigates a gate-based algorithm for this purpose, the Quantum Approximate Optimization Algorithm (QAOA), in two major themes. First, we examine how the QAOA resolves the problems it is designed to solve. We take a statistical view of the algorithm applied to ensembles of problems, first, considering a highly symmetric version of the algorithm, using Grover drivers. In this highly symmetric context, we find a simple dependence of the QAOA stateâs expected value on how values of the cost function are distributed. Furthering this theme, we demonstrate that, generally, QAOA performance depends on problem statistics with respect to a metric induced by a chosen driver Hamiltonian. We obtain a method for evaluating QAOA performance on worst-case problems, those of random costs, for differing driver choices. Second, we investigate a QAOA context with device control occurring only via single-qubit gates, rather than using individually programmable one- and two-qubit gates. In this reduced control overhead scheme---the digital-analog scheme---the complexity of devices running QAOA circuits is decreased at the cost of errors which are shown to be non-harmful in certain regimes. We then explore hypothetical device designs one could use for this purpose.Eine mögliche Anwendung fĂŒr âNoisy Intermediate-Scale Quantum devicesâ (NISQ devices) ist die nĂ€herungsweise Lösung von kombinatorischen Optimierungsproblemen. Die vorliegende Arbeit untersucht anhand zweier Hauptthemen einen gatterbasierten Algorithmus, den sogenannten âQuantum Approximate Optimization Algorithmâ (QAOA). Zuerst prĂŒfen wir, wie der QAOA jene Probleme löst, fĂŒr die er entwickelt wurde. Wir betrachten den Algorithmus in einer Kombination mit hochsymmetrischen Grover-Treibern fĂŒr statistische Ensembles von Probleminstanzen. In diesem Kontext finden wir eine einfache AbhĂ€ngigkeit von der Verteilung der Kostenfunktionswerte. WeiterfĂŒhrend zeigen wir, dass die QAOA-Leistung generell von der Problemstatistik in Bezug auf eine durch den gewĂ€hlten Treiber-Hamiltonian induzierte Metrik abhĂ€ngt. Wir erhalten eine Methode zur Bewertung der QAOA-Leistung bei schwersten Problemen (solche zufĂ€lliger Kosten) fĂŒr unterschiedliche Treiberauswahlen. Zweitens untersuchen wir eine QAOA-Variante, bei der sich die Hardware- Kontrolle nur auf Ein-Qubit-Gatter anstatt individuell programmierbare Ein- und Zwei-Qubit-Gatter erstreckt. In diesem reduzierten Kontrollaufwandsschemaâdem digital-analogen Schemaâsinkt die KomplexitĂ€t der Hardware, welche die QAOASchaltungen ausfĂŒhrt, auf Kosten von Fehlern, die in bestimmten Bereichen als ungefĂ€hrlich nachgewiesen werden. Danach erkunden wir hypothetische Hardware- Konzepte, die fĂŒr diesen Zweck genutzt werden könnten
Gap Amplification for Reconfiguration Problems
In this paper, we demonstrate gap amplification for reconfiguration problems.
In particular, we prove an explicit factor of PSPACE-hardness of approximation
for three popular reconfiguration problems only assuming the Reconfiguration
Inapproximability Hypothesis (RIH) due to Ohsaka (STACS 2023). Our main result
is that under RIH, Maxmin Binary CSP Reconfiguration is PSPACE-hard to
approximate within a factor of . Moreover, the same result holds even
if the constraint graph is restricted to -expander for arbitrarily
small . The crux of its proof is an alteration of the gap
amplification technique due to Dinur (J. ACM, 2007), which amplifies the
vs. gap for arbitrarily small up to the vs.
gap. As an application of the main result, we demonstrate that
Minmax Set Cover Reconfiguration and Minmax Dominating Set Reconfiguratio} are
PSPACE-hard to approximate within a factor of under RIH. Our proof is
based on a gap-preserving reduction from Label Cover to Set Cover due to Lund
and Yannakakis (J. ACM, 1994). However, unlike Lund--Yannakakis' reduction, the
expander mixing lemma is essential to use. We highlight that all results hold
unconditionally as long as "PSPACE-hard" is replaced by "NP-hard," and are the
first explicit inapproximability results for reconfiguration problems without
resorting to the parallel repetition theorem. We finally complement the main
result by showing that it is NP-hard to approximate Maxmin Binary CSP
Reconfiguration within a factor better than .Comment: 41 pages, to appear in Proc. 35th Annu. ACM-SIAM Symp. Discrete
Algorithms (SODA), 202
VĂ©rification efficace de systĂšmes Ă compteurs Ă l'aide de relaxations
Abstract : Counter systems are popular models used to reason about systems in various fields such as the analysis of concurrent or distributed programs and the discovery and verification of business processes. We study well-established problems on various classes of counter systems. This thesis focusses on three particular systems, namely Petri nets, which are a type of model for discrete systems with concurrent and sequential events, workflow nets, which form a subclass of Petri nets that is suited for modelling and reasoning about business processes, and continuous one-counter automata, a novel model that combines continuous semantics with one-counter automata. For Petri nets, we focus on reachability and coverability properties. We utilize directed search algorithms, using relaxations of Petri nets as heuristics, to obtain novel semi-decision algorithms for reachability and coverability, and positively evaluate a prototype implementation. For workflow nets, we focus on the problem of soundness, a well-established correctness notion for such nets. We precisely characterize the previously widely-open complexity of three variants of soundness. Based on our insights, we develop techniques to verify soundness in practice, based on reachability relaxation of Petri nets. Lastly, we introduce the novel model of continuous one-counter automata. This model is a natural variant of one-counter automata, which allows reasoning in a hybrid manner combining continuous and discrete elements. We characterize the exact complexity of the reachability problem in several variants of the model.Les systÚmes à compteurs sont des modÚles utilisés afin de raisonner sur les systÚmes
de divers domaines tels lâanalyse de programmes concurrents ou distribuĂ©s, et
la dĂ©couverte et la vĂ©rification de systĂšmes dâaffaires. Nous Ă©tudions des problĂšmes
bien établis de différentes classes de systÚmes à compteurs. Cette thÚse se penche sur
trois systĂšmes particuliers : les rĂ©seaux de Petri, qui sont un type de modĂšle pour les systĂšmes discrets Ă
événements concurrents et séquentiels ; les « réseaux de processus », qui forment une sous-classe des réseaux de Petri
adaptĂ©e Ă la modĂ©lisation et au raisonnement des processus dâaffaires ; les automates continus Ă un compteur, un nouveau modĂšle qui combine une
sémantique continue à celles des automates à un compteur.
Pour les rĂ©seaux de Petri, nous nous concentrons sur les propriĂ©tĂ©s dâaccessibilitĂ©
et de couverture. Nous utilisons des algorithmes de parcours de graphes, avec
des relaxations de rĂ©seaux de Petri comme heuristiques, afin dâobtenir de nouveaux
algorithmes de semi-dĂ©cision pour lâaccessibilitĂ© et la couverture, et nous Ă©valuons
positivement un prototype.
Pour les «réseaux de processus», nous nous concentrons sur le problÚme de validité,
une notion de correction bien établie pour ces réseaux. Nous caractérisions
prĂ©cisĂ©ment la complexitĂ© calculatoire jusquâici largement ouverte de trois variantes
du problÚme de validité. En nous basant sur nos résultats, nous développons des techniques
pour vĂ©rifier la validitĂ© en pratique, Ă lâaide de relaxations dâaccessibilitĂ© dans
les rĂ©seaux de Petri. Enfin, nous introduisons le nouveau modĂšle dâautomates continus Ă un compteur. Ce modĂšle est une variante naturelle des automates Ă un compteur, qui permet de
raisonner de maniÚre hybride en combinant des éléments continus et discrets. Nous
caractĂ©risons la complexitĂ© exacte du problĂšme dâaccessibilitĂ© dans plusieurs variantes
du modĂšle
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