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We present an industrial end-user perspective on the current state of quantum computing hardware for one specific technological approach, the neutral atom platform. Our aim is to assist developers in understanding the impact of the specific properties of these devices on the effectiveness of algorithm execution. Based on discussions with different vendors and recent literature, we discuss the performance data of the neutral atom platform. Specifically, we focus on the physical qubit architecture, which affects state preparation, qubit-to-qubit connectivity, gate fidelities, native gate instruction set, and individual qubit stability. These factors determine both the quantum-part execution time and the end-to-end wall clock time relevant for end-users, but also the ability to perform fault-tolerant quantum computation in the future. We end with an overview of which applications have been shown to be well suited for the peculiar properties of neutral atom-based quantum computers.
The prospect of achieving computational speedups by exploiting quantum phenomena makes the use of quantum processing units (QPUs) attractive for many algorithmic database problems. Query optimisation, which concerns problems that typically need to explore large search spaces, seems like an ideal match for the known quantum algorithms. We present the first quantum implementation of join ordering, which is one of the most investigated and fundamental query optimisation problems, based on a reformulation to quadratic binary unconstrained optimisation problems. We empirically characterise our method on two state-of-the-art approaches (gate-based quantum computing and quantum annealing), and identify speed-ups compared to the best know classical join ordering approaches for input sizes that can be processed with current quantum annealers. However, we also confirm that limits of early-stage technology are quickly reached.
Current QPUs are classified as noisy, intermediate scale quantum computers (NISQ), and are restricted by a variety of limitations that reduce their capabilities as compared to ideal future quantum computers, which prevents us from scaling up problem dimensions and reaching practical utility. To overcome these challenges, our formulation accounts for specific QPU properties and limitations, and allows us to trade between achievable solution quality and possible problem size.
In contrast to all prior work on quantum computing for query optimisation and database-related challenges, we go beyond currently available QPUs, and explicitly target the scalability limitations: Using insights gained from numerical simulations and our experimental analysis, we identify key criteria for co-designing QPUs to improve their usefulness for join ordering, and show how even relatively minor physical architectural improvements can result in substantial enhancements. Finally, we outline a path towards practical utility of custom-designed QPUs.
We evaluate the applicability of quantum computing on two fundamental query optimization problems, join order optimization and multi query optimization (MQO). We analyze the problem dimensions that can be solved on current gate-based quantum systems and quantum annealers, the two currently commercially available architectures.
First, we evaluate the use of gate-based systems on MQO, previously solved with quantum annealing. We show that, contrary to classical computing, a different architecture requires involved adaptations. We moreover propose a multi-step reformulation for join ordering problems to make them solvable on current quantum systems. Finally, we systematically evaluate our contributions for gate-based quantum systems and quantum annealers. Doing so, we identify the scope of current limitations, as well as the future potential of quantum computing technologies for database systems.
We propose a quantum key distribution scheme which closely matches the performance of a perfect single photon source. It nearly attains the physical upper bound in terms of key generation rate and maximally achievable distance. Our scheme relies on a practical setup based on a parametric downconversion source and present day, nonideal photon-number detection. Arbitrary experimental imperfections which lead to bit errors are included. We select decoy states by classical postprocessing. This allows one to improve the effective signal statistics and achievable distance.
Quantum key distribution is among the foremost applications of quantum mechanics, both in terms of fundamental physics and as a technology on the brink of commercial deployment. Starting from principal schemes and initial proofs of unconditional security for perfect systems, much effort has gone into providing secure schemes which can cope with numerous experimental imperfections unavoidable in real world implementations. In this paper, we provide a comparison of various schemes and protocols. We analyse their efficiency and performance when implemented with imperfect physical components. We consider how experimental faults are accounted for using effective parameters. We compare various recent protocols and provide guidelines as to which components propose best advances when being improved.
We experimentally analyze the complete photon number statistics of parametric down-conversion and ascertain the influence of multimode effects. Our results clearly reveal a difference between single-mode theoretical description and the measured distributions. Further investigations assure the applicability of loss-tolerant photon number reconstruction and prove strict photon number correlation between signal and idler modes.
Every security analysis of quantum-key distribution (QKD) relies on a faithful modeling of the employed quantum states. Many photon sources, such as for instance a parametric down-conversion (PDC) source, require a multimode description but are usually only considered in a single-mode representation. In general, the important claim in decoy-based QKD protocols for indistinguishability between signal and decoy states does not hold for all sources. We derive bounds on the single-photon transmission probability and error rate for multimode states and apply these bounds to the output state of a PDC source. We observe two opposing effects on the secure key rate. First, the multimode structure of the state gives rise to a new attack that decreases the key rate. Second, more contributing modes change the photon number distribution from a thermal toward a Poissonian distribution, which increases the key rate.
Random numbers are a valuable component in diverse applications that range from simulations over gambling to cryptography. The quest for true randomness in these applications has engendered a large variety of different proposals for producing random numbers based on the foundational unpredictability of quantum mechanics4,5,6,7,8,9,10,11. However, most approaches do not consider that a potential adversary could have knowledge about the generated numbers, so the numbers are not verifiably random and unique12,13,14,15. Here we present a simple experimental setup based on homodyne measurements that uses the purity of a continuous-variable quantum vacuum state to generate unique random numbers. We use the intrinsic randomness in measuring the quadratures of a mode in the lowest energy vacuum state, which cannot be correlated to any other state. The simplicity of our source, combined with its verifiably unique randomness, are important attributes for achieving high-reliability, high-speed and low-cost quantum random number generators.
Wer seine Daten mit ansehnlichen und informativen Graphen veranschaulichen möchte, braucht meist viel Geduld. Die R-Erweiterung Ggplot2 bringt System in die Grafik, drückt sich in knappem Quellcode aus und bläst frischen Wind in den Alltag der Datenvisualisierung.
We discuss the spectral structure and decomposition of multi-photon states. Ordinarily 'multi-photon states' and 'Fock states' are regarded as synonymous. However, when the spectral degrees of freedom are included this is not the case, and the class of 'multi-photon' states is much broader than the class of 'Fock' states. We discuss the criteria for a state to be considered a Fock state. We then address the decomposition of general multi-photon states into bases of orthogonal eigenmodes, building on existing multi-mode theory, and introduce an occupation number representation that provides an elegant description of such states. This representation allows us to work in bases imposed by experimental constraints, simplifying calculations in many situations. Finally we apply this technique to several example situations, which are highly relevant for state of the art experiments. These include Hong–Ou–Mandel interference, spectral filtering, finite bandwidth photo-detection, homodyne detection and the conditional preparation of Schrödinger kitten and Fock states. Our techniques allow for very simple descriptions of each of these examples.
Parametric down-conversion (PDC) is a technique of ubiquitous experimental significance in the production of nonclassical, photon-number-correlated twin beams. Standard theory of PDC as a two-mode squeezing process predicts and homodyne measurements observe a thermal photon number distribution per beam. Recent experiments have obtained conflicting distributions. In this article, we explain the observation by an a priori theoretical model solely based on directly accessible physical quantities. We compare our predictions with experimental data and find excellent agreement.
Measurement is the only part of a general quantum system that has yet to be characterised experimentally in a complete manner. Detector tomography provides a procedure for doing just this; an arbitrary measurement device can be fully characterised, and thus calibrated, in a systematic way without access to its components or its design. The result is a reconstructed POVM containing the measurement operators associated with each measurement outcome. We consider two detectors, a single-photon detector and a photon-number counter, and propose an easily realised experimental apparatus to perform detector tomography on them. We also present a method of visualising the resulting measurement operators.
Software evolution is a fundamental process that transcends the realm of technical artifacts and permeates the entire organizational structure of a software project. By means of a longitudinal empirical study of 18 large open-source projects, we examine and discuss the evolutionary principles that govern the coordination of developers. By applying a network-analytic approach, we found that the implicit and self-organizing structure of developer coordination is ubiquitously described by non-random organizational principles that defy conventional software-engineering wisdom. In particular, we found that: (a) developers form scale-free networks, in which the majority of coordination requirements arise among an extremely small number of developers, (b) developers tend to accumulate coordination requirements with more and more developers over time, presumably limited by an upper bound, and (c) initially developers are hierarchically arranged, but over time, form a hybrid structure, in which core developers are hierarchically arranged and peripheral developers are not. Our results suggest that the organizational structure of large projects is constrained to evolve towards a state that balances the costs and benefits of developer coordination, and the mechanisms used to achieve this state depend on the project’s scale.
Die wissenschaftliche Reproduktionskrise hat den Blick auf digitale Forschungswerkzeuge intensiviert. Auch wenn der Mehraufwand für Reproduzierbarkeit und Zugänglichkeit zunehmend anerkannt wird, existieren noch Defizite in der Umsetzung, wenn es darum geht, die Datenbasis und Forschungswerkzeuge verfügbar zu machen
Many industrially relevant problems can be deterministically solved by computers in principle, but are intractable in practice, as the seminal P/NP dichotomy of complexity theory and Cobham’s thesis testify. For the many NP-complete problems, industry needs to resort to using heuristics or approximation algorithms. For approximation algorithms, there is a more refined classification in complexity classes that goes beyond the simple P/NP dichotomy. As it is well known, approximation classes form a hierarchy, that is, FPTAS \subseteq PTAS \subseteq APX \subseteq NPO. This classification gives a more realistic notion of complexity but—unless unexpected breakthroughs happen for fundamental problems like P = NP or related questions— there is no known efficient algorithm that can solve such problems exactly on a realistic computer. Therefore, new ways of computations are sought. Recently, considerable hope was placed on the possible computational powers of quantum computers and quantum annealing (QA) in particular. However, the precise benefits of such a drastic shift in hardware are still unchartered territory to a good extent. Firstly, the exact relations between classical and quantum complexity classes pose many open questions, and secondly, technical details of formulating and implementing quantum algorithms play a crucial role in real-world applications. Guided by the hierarchy of classical optimisation complexity classes, we discuss how to map problems of each class to a quantum annealer. Those problems are the Minimum Multiprocessor Scheduling (MMS) problem, the Minimum Vertex Cover (MVC) problem and the Maximum Independent Set (MIS) problem. We experimentally investigate if and how the degree of approximability influences implementation and run-time performance. Our experiments indicate a discrepancy between classical approximation complexity and QA behaviour: Problems MIS and MVC, members of APX respectively PTAS, exhibit better solution quality on a QA than MMS, which is in FPTAS, even despite the use of preprocessing the for latter. This leads to the hypothesis that traditional classifications do not immediately extend to the quantum annealing domain, at least when the properties of real-world devices are taken into account. A structural reason, why FPTAS problems do not show good solution quality, might be the use of an inequlity in the problem description of the FPTAS problems. Formulating those inequalities on a quantum hardware (mostly done by formulating a Quadratic Unconstrained Binary optimisation (QUBO) problem in form of a matrix) requires a lot of hardware space which makes finding an optimal solution more difficult. Reducing the density of a QUBO is possible by appropriately pruning QUBO matrices. For the problems considered in our evaluation, we find that the achievable solution quality on a real-world machine is unexpectedly robust against pruning, often up to ratios as high as 50% or more. Since quantum annealers are probabilistic machines by design, the loss in solution quality is only of subordinate relevance, especially considering that the pruning of QUBO matrices allows for solving larger problem instances on hardware of a given capacity. We quantitatively discuss the interplay between these factors.
Deep Reinforcement Learning (RL) has considerably advanced over the past decade. At the same time, state-of-the-art RL algorithms require a large computational budget in terms of training time to converge. Recent work has started to approach this problem through the lens of quantum computing, which promises theoretical speed-ups for several traditionally hard tasks. In this work, we examine a class of hybrid quantumclassical RL algorithms that we collectively refer to as variational quantum deep Q-networks (VQ-DQN). We show that VQ-DQN approaches are subject to instabilities that cause the learned policy to diverge, study the extent to which this afflicts reproduciblity of established results based on classical simulation, and perform systematic experiments to identify potential explanations for the observed instabilities. Additionally, and in contrast to most existing work on quantum reinforcement learning, we execute RL algorithms on an actual quantum processing unit (an IBM Quantum Device) and investigate differences in behaviour between simulated and physical quantum systems that suffer from implementation deficiencies. Our experiments show that, contrary to opposite claims in the literature, it cannot be conclusively decided if known quantum approaches, even if simulated without physical imperfections, can provide an advantage as compared to classical approaches. Finally, we provide a robust, universal and well-tested implementation of VQ-DQN as a reproducible testbed for future experiments.
Quantum computing promises to overcome computational limitations with better and faster solutions for optimization, simulation, and machine learning problems. Europe and Germany are in the process of successfully establishing research and funding programs with the objective to dvance the technology’s ecosystem and industrialization, thereby ensuring digital sovereignty, security, and competitiveness. Such an ecosystem comprises hardware/software solution providers, system integrators, and users from research institutions, start-ups, and industry. The vision of the Quantum Technology and Application Consortium (QUTAC) is to establish and advance the quantum computing ecosystem, supporting the ambitious goals of the German government and various research programs. QUTAC is comprised of ten members representing different industries, in particular automotive manufacturing, chemical and pharmaceutical production, insurance, and technology. In this paper, we survey the current state of quantum computing in these sectors as well as the aerospace industry and identify the contributions of QUTAC to the ecosystem. We propose an application-centric approach for the industrialization of the technology based on proven business impact. This paper identifies 24 different use cases. By formalizing high-value use cases into well-described reference problems and benchmarks, we will guide technological progress and eventually commercialization. Our results will be beneficial to all ecosystem participants, including suppliers, system integrators, software developers, users, policymakers, funding program managers, and investors.
A Hybrid Solution Method for the Capacitated Vehicle Routing Problem Using a Quantum Annealer
(2019)
he Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem (NPO) that has been of great interest for decades for both, science and industry. The CVRP is a variant of the vehicle routing problem characterized by capacity constrained vehicles. The aim is to plan tours for vehicles to supply a given number of customers as efficiently as possible. The problem is the combinatorial explosion of possible solutions, which increases superexponentially with the number of customers. Classical solutions provide good approximations to the globally optimal solution. D-Wave's quantum annealer is a machine designed to solve optimization problems. This machine uses quantum effects to speed up computation time compared to classic computers. The problem on solving the CVRP on the quantum annealer is the particular formulation of the optimization problem. For this, it has to be mapped onto a quadratic unconstrained binary optimization (QUBO) problem. Complex optimization problems such as the CVRP can be translated to smaller subproblems and thus enable a sequential solution of the partitioned problem. This work presents a quantum-classic hybrid solution method for the CVRP. It clarifies whether the implementation of such a method pays off in comparison to existing classical solution methods regarding computation time and solution quality. Several approaches to solving the CVRP are elaborated, the arising problems are discussed, and the results are evaluated in terms of solution quality and computation time.
This paper describes a large-scale empirical study investigating the relevance of socio-technical congruence over key basic software quality metrics, namely, bugs and churn. That is, we explore whether alignment or misalignment of social communication structures and technical dependencies in large software projects influences software quality. To this end, we have defined a quantitative and operational notion of socio-technical congruence, which we call /socio-technical motif congruence/ (STMC). STMC is a measure of the degree to which developers working on the same file or on two related files, need to communicate. As socio-technical congruence is a complex and multi-faceted phenomenon, the interpretability of the results is one of our main concerns, so we have employed a careful mixed-methods statistical analysis. In particular, we provide analyses with similar techniques as employed by seminal work in the field to ensure comparability of our results with the existing body of work. The major result of our study, based on an analysis of 25 large open-source projects, is that STMC is /not/ related to project quality measures---software bugs and churn---in any temporal scenario. That is, we find no statistical relationship between the alignment of developer tasks and developer communications on one hand, and project outcomes on the other hand. We conclude that, wherefore congruence does matter as literature shows, then its measurable effect lies elsewhere.