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Distributed Quantum Computing (DQC) provides a means for scaling available quantum computation by interconnecting multiple quantum processor units (QPUs). A key challenge in this domain is efficiently allocating logical qubits from quantum circuits to the physical qubits within QPUs, a task known to be NP-hard. Traditional approaches, primarily focused on graph partitioning strategies, have sought to reduce the number of required Bell pairs for executing non-local CNOT operations, a form of gate teleportation. However, these methods have limitations in terms of efficiency and scalability. Addressing this, our work jointly considers gate and qubit teleportations introducing a novel meta-heuristic algorithm to minimise the network cost of executing a quantum circuit. By allowing dynamic reallocation of qubits along with gate teleportations during circuit execution, our method significantly enhances the overall efficacy and potential scalability of DQC frameworks. In our numerical analysis, we demonstrate that integrating qubit teleportations into our genetic algorithm for optimising circuit blocking reduces the required resources, specifically the number of EPR pairs, compared to traditional graph partitioning methods. Our results, derived from both benchmark and randomly generated circuits, show that as circuit complexity increases - demanding more qubit teleportations - our approach effectively optimises these teleportations throughout the execution, thereby enhancing performance through strategic circuit partitioning. This is a step forward in the pursuit of a global quantum compiler which will ultimately enable the efficient use of a 'quantum data center' in the future., Comment: 9 pages, 9 figures

The practical realization of quantum programs that require large-scale qubit systems is hindered by current technological limitations. Distributed Quantum Computing (DQC) presents a viable path to scalability by interconnecting multiple Quantum Processing Units (QPUs) through quantum links, facilitating the distributed execution of quantum circuits. In DQC, EPR pairs are generated and shared between distant QPUs, which enables quantum teleportation and facilitates the seamless execution of circuits. A primary obstacle in DQC is the efficient mapping and routing of logical qubits to physical qubits across different QPUs, necessitating sophisticated strategies to overcome hardware constraints and optimize communication. We introduce a novel compiler that, unlike existing approaches, prioritizes reducing the expected execution time by jointly managing the generation and routing of EPR pairs, scheduling remote operations, and injecting SWAP gates to facilitate the execution of local gates. We present a real-time, adaptive approach to compiler design, accounting for the stochastic nature of entanglement generation and the operational demands of quantum circuits. Our contributions are twofold: (i) we model the optimal compiler for DQC using a Markov Decision Process (MDP) formulation, establishing the existence of an optimal algorithm, and (ii) we introduce a constrained Reinforcement Learning (RL) method to approximate this optimal compiler, tailored to the complexities of DQC environments. Our simulations demonstrate that Double Deep Q-Networks (DDQNs) are effective in learning policies that minimize the depth of the compiled circuit, leading to a lower expected execution time and likelihood of successful operation before qubits decohere.

The Gottesman-Kitaev-Preskill (GKP) code, being information theoretically near optimal for quantum communication over Gaussian thermal-loss optical channels, is likely to be the encoding of choice for advanced quantum networks of the future. Quantum repeaters based on GKP-encoded light have been shown to support high end-to-end entanglement rates across large distances despite realistic finite squeezing in GKP code preparation and homodyne detection inefficiencies. Here, we introduce a quantum switch for GKP-qubit-based quantum networks, whose architecture involves multiplexed GKP-qubit-based entanglement link generation with clients, and their all-photonic storage, together enabled by GKP-qubit graph state resources. For bipartite entanglement distribution between clients via entanglement swapping, the switch uses a multi-client generalization of a recently introduced $\textit{entanglement-ranking-based link matching}$ protocol heuristic. Since generating the GKP-qubit graph state resource is hardware intensive, given a total resource budget and an arbitrary layout of clients, we address the question of their optimal allocation towards the different client-pair connections served by the switch such that the sum throughput of the switch is maximized while also being fair in terms of the individual entanglement rates. We illustrate our results for an exemplary data center network, where the data center is a client of a switch and all of its other clients aim to connect to the data center alone -- a scenario that also captures the general case of a gateway router connecting a local area network to a global network. Together with compatible quantum repeaters, our quantum switch provides a way to realize quantum networks of arbitrary topology., Comment: 13 pages, 8 Figures

The quantum nature of light enables potentially revolutionary communication technologies. Key to advancing this area of research is a clear understanding of the concepts of states, modes, fields, and photons. The concept of field modes carries over from classical optics, while the concept of state has to be considered carefully when treating light quantum mechanically. The term 'photon' is an overloaded identifier in the sense that it is often used to refer to either a quantum particle or the state of a field. This overloading, often used without placing in context, has the potential to obfuscate the physical processes that describe the reality we measure. We review the uses and relationships between these concepts using modern quantum optics theory, including the concept of a photon wave function, the modern history of which was moved forward in a groundbreaking paper in this journal by Iwo Bia{\l}ynicki-Birula, to whom this article is dedicated., Comment: This article belongs to the special issue of Acta Physica Polonica A printed in honor of Professor Iwo Bialynicki-Birula on the occasion of his 90th birthday (Ed. Tomasz Sowinski, DOI:10.12693/APhysPolA.143.S0)

Long distance quantum communication will require the use of quantum repeaters to overcome the exponential attenuation of signal with distance. One class of such repeaters utilizes quantum error correction to overcome losses in the communication channel. Here we propose a novel strategy of using the bosonic Gottesman-Kitaev-Preskill (GKP) code in a two-way repeater architecture with multiplexing. The crucial feature of the GKP code that we make use of is the fact that GKP qubits easily admit deterministic two-qubit gates, hence allowing for multiplexing without the need for generating large cluster states as required in previous all-photonic architectures based on discrete-variable codes. Moreover, alleviating the need for such clique-clusters entails that we are no longer limited to extraction of at most one end-to-end entangled pair from a single protocol run. In fact, thanks to the availability of the analog information generated during the measurements of the GKP qubits, we can design better entanglement swapping procedures in which we connect links based on their estimated quality. This enables us to use all the multiplexed links so that large number of links from a single protocol run can contribute to the generation of the end-to-end entanglement. We find that our architecture allows for high-rate end-to-end entanglement generation and is resilient to imperfections arising from finite squeezing in the GKP state preparation and homodyne detection inefficiency. In particular we show that long-distance quantum communication over more than 1000 km is possible even with less than 13 dB of GKP squeezing. We also quantify the number of GKP qubits needed for the implementation of our scheme and find that for good hardware parameters our scheme requires around $10^3-10^4$ GKP qubits per repeater per protocol run., Comment: v3 as published, 34 + 24 pages, 40 figures, corrected typos in some equations in Appendix G

Cloud computing with its three key facets (i.e., IaaS, PaaS, and SaaS) and its inherent advantages (e.g., elasticity and scalability) still faces several challenges. The distance between the cloud and the end devices might be an issue for latency-sensitive applications such as disaster management and content delivery applications. Service Level Agreements (SLAs) may also impose processing at locations where the cloud provider does not have data centers. Fog computing is a novel paradigm to address such issues. It enables provisioning resources and services outside the cloud, at the edge of the network, closer to end devices or eventually, at locations stipulated by SLAs. Fog computing is not a substitute for cloud computing but a powerful complement. It enables processing at the edge while still offering the possibility to interact with the cloud. This article presents a comprehensive survey on fog computing. It critically reviews the state of the art in the light of a concise set of evaluation criteria. We cover both the architectures and the algorithms that make fog systems. Challenges and research directions are also introduced. In addition, the lessons learned are reviewed and the prospects are discussed in terms of the key role fog is likely to play in emerging technologies such as Tactile Internet.

In large-scale natural disasters, humans are likely to fail when they attempt to reach high-risk sites or act in search and rescue operations. Robots, however, outdo their counterparts in surviving the hazards and handling the search and rescue missions due to their multiple and diverse sensing and actuation capabilities. The dynamic formation of optimal coalition of these heterogeneous robots for cost efficiency is very challenging and research in the area is gaining more and more attention. In this paper, we propose a novel heuristic. Since the population of robots in large-scale disaster settings is very large, we rely on Quantum Multi-Objective Particle Swarm Optimization (QMOPSO). The problem is modeled as a multi-objective optimization problem. Simulations with different test cases and metrics, and comparison with other algorithms such as NSGA-II and SPEA-II are carried out. The experimental results show that the proposed algorithm outperforms the existing algorithms not only in terms of convergence but also in terms of diversity and processing time.

Virtualization enables multiple applications to share the same wireless sensor and actuator network (WSAN). However, in heterogeneous environments, virtualized wireless sensor and actuator networks (VWSAN) raise new challenges, such as the need for on-the-fly, dynamic, elastic, and scalable provisioning of gateways. Network Functions Virtualization (NFV) is a paradigm emerging to help tackle these new challenges. It leverages standard virtualization technology to consolidate special-purpose network elements on commodity hardware. This article presents NFV architecture for VWSAN gateways, in which software instances of gateway modules are hosted in NFV infrastructure operated and managed by a VWSAN gateway provider. We consider several VWSAN providers, each with its own brand or combination of brands of sensors and actuators/robots. These sensors and actuators can be accessed by a variety of applications, each may have different interface and QoS (i.e., latency, throughput, etc.) requirements. The NFV infrastructure allows dynamic, elastic, and scalable deployment of gateway modules in this heterogeneous VWSAN environment. Furthermore, the proposed architecture is flexible enough to easily allow new sensors and actuators integration and new application domains accommodation. We present a prototype that is built using the OpenStack platform. Besides, the performance results are discussed

Virtualization enables the sharing of a same wireless sensor network (WSN) by multiple applications. However, in heterogeneous environments, virtualized wireless sensor networks (VWSN) raises new challenges such as the need for on-the-fly, dynamic, elastic and scalable provisioning of gateways. Network Functions Virtualization (NFV) is an emerging paradigm that can certainly aid in tackling these new challenges. It leverages standard virtualization technology to consolidate special-purpose network elements on top of commodity hardware. This article presents a case study on NFV based gateways for VWSNs. In the study, a VWSN gateway provider, operates and manages an NFV based infrastructure. We use two different brands of wireless sensors. The NFV infrastructure makes possible the dynamic, elastic and scalable deployment of gateway modules in this heterogeneous VWSN environment. The prototype built with Openstack as platform is described.

Wireless sensor networks (WSNs) have become pervasive and are used in many applications and services. Usually the deployments of WSNs are task oriented and domain specific; thereby precluding re-use when other applications and services are contemplated. This inevitably leads to the proliferation of redundant WSN deployments. Virtualization is a technology that can aid in tackling this issue, as it enables the sharing of resources/infrastructure by multiple independent entities. In this paper we critically review the state of the art and propose a novel architecture for WSN virtualization. The proposed architecture has four layers (physical layer, virtual sensor layer, virtual sensor access layer and overlay layer) and relies on the constrained application protocol (CoAP). We illustrate its potential by using it in a scenario where a single WSN is shared by multiple applications; one of which is a fire monitoring application. We present the proof-of-concept prototype we have built along with the performance measurements, and discuss future research directions., Comment: Accepted for publication on June 27th 2014 in Forthcoming issue of IEEE Network Magazine (May/June 2015 issue)