Distributed Approximation Algorithms for Weighted Shortest Paths

A distributed network is modeled by a graph having $n$ nodes (processors) and diameter $D$. We study the time complexity of approximating {\em weighted} (undirected) shortest paths on distributed networks with a $O(\log n)$ {\em bandwidth restriction} on edges (the standard synchronous \congest model). The question whether approximation algorithms help speed up the shortest paths (more precisely distance computation) was raised since at least 2004 by Elkin (SIGACT News 2004). The unweighted case of this problem is well-understood while its weighted counterpart is fundamental problem in the area of distributed approximation algorithms and remains widely open. We present new algorithms for computing both single-source shortest paths (\sssp) and all-pairs shortest paths (\apsp) in the weighted case. Our main result is an algorithm for \sssp. Previous results are the classic $O(n)$-time Bellman-Ford algorithm and an $\tilde O(n^{1/2+1/2k}+D)$-time $(8k\lceil \log (k+1) \rceil -1)$-approximation algorithm, for any integer $k\geq 1$, which follows from the result of Lenzen and Patt-Shamir (STOC 2013). (Note that Lenzen and Patt-Shamir in fact solve a harder problem, and we use $\tilde O(\cdot)$ to hide the O(\poly\log n) term.) We present an $\tilde O(n^{1/2}D^{1/4}+D)$-time $(1+o(1))$-approximation algorithm for \sssp. This algorithm is {\em sublinear-time} as long as $D$ is sublinear, thus yielding a sublinear-time algorithm with almost optimal solution. When $D$ is small, our running time matches the lower bound of $\tilde \Omega(n^{1/2}+D)$ by Das Sarma et al. (SICOMP 2012), which holds even when $D=\Theta(\log n)$, up to a \poly\log n factor.Comment: Full version of STOC 201

Nature-Inspired Interconnects for Self-Assembled Large-Scale Network-on-Chip Designs

Future nano-scale electronics built up from an Avogadro number of components needs efficient, highly scalable, and robust means of communication in order to be competitive with traditional silicon approaches. In recent years, the Networks-on-Chip (NoC) paradigm emerged as a promising solution to interconnect challenges in silicon-based electronics. Current NoC architectures are either highly regular or fully customized, both of which represent implausible assumptions for emerging bottom-up self-assembled molecular electronics that are generally assumed to have a high degree of irregularity and imperfection. Here, we pragmatically and experimentally investigate important design trade-offs and properties of an irregular, abstract, yet physically plausible 3D small-world interconnect fabric that is inspired by modern network-on-chip paradigms. We vary the framework's key parameters, such as the connectivity, the number of switch nodes, the distribution of long- versus short-range connections, and measure the network's relevant communication characteristics. We further explore the robustness against link failures and the ability and efficiency to solve a simple toy problem, the synchronization task. The results confirm that (1) computation in irregular assemblies is a promising and disruptive computing paradigm for self-assembled nano-scale electronics and (2) that 3D small-world interconnect fabrics with a power-law decaying distribution of shortcut lengths are physically plausible and have major advantages over local 2D and 3D regular topologies

Topology Adaption for the Quantum Internet

In the quantum repeater networks of the quantum Internet, the varying stability of entangled quantum links makes dynamic topology adaption an emerging issue. Here we define an efficient topology adaption method for quantum repeater networks. The model assumes the random failures of entangled links and several parallel demands from legal users. The shortest path defines a set of entangled links for which the probability of stability is above a critical threshold. The scheme is utilized in a base-graph of the overlay quantum network to provide an efficient shortest path selection for the demands of all users of the network. We study the problem of entanglement assignment in a quantum repeater network, prove its computational complexity, and show an optimization procedure. The results are particularly convenient for future quantum networking, quantum-Internet, and experimental long-distance quantum communications.Comment: 17 pages, Journal-ref: Quant. Inf. Proc. (2018

Deterministic delivery of remote entanglement on a quantum network

Large-scale quantum networks promise to enable secure communication, distributed quantum computing, enhanced sensing and fundamental tests of quantum mechanics through the distribution of entanglement across nodes. Moving beyond current two-node networks requires the rate of entanglement generation between nodes to exceed their decoherence rates. Beyond this critical threshold, intrinsically probabilistic entangling protocols can be subsumed into a powerful building block that deterministically provides remote entangled links at pre-specified times. Here we surpass this threshold using diamond spin qubit nodes separated by 2 metres. We realise a fully heralded single-photon entanglement protocol that achieves entangling rates up to 39 Hz, three orders of magnitude higher than previously demonstrated two-photon protocols on this platform. At the same time, we suppress the decoherence rate of remote entangled states to 5 Hz by dynamical decoupling. By combining these results with efficient charge-state control and mitigation of spectral diffusion, we are able to deterministically deliver a fresh remote state with average entanglement fidelity exceeding 0.5 at every clock cycle of $\sim$100 ms without any pre- or post-selection. These results demonstrate a key building block for extended quantum networks and open the door to entanglement distribution across multiple remote nodes.Comment: v2 - updated to include relevant citatio

Optimal Remote Qubit Teleportation Using Node2vec

Much research work is done on implementing quantum teleportation and entanglement swapping for remote entanglement. Due to dynamical topological changes in quantum networks, nodes have to construct the shortest paths every time they want to communicate with a remote neighbour. But due to the entanglement failures remote entanglement establishment is still a challenging task. Also as the nodes know only about their neighbouring nodes computing optimal paths between source and remote nodes is time consuming too. In finding the next best neighbour in the optimal path between a given source and remote nodes so as to decrease the entanglement cost, deep learning techniques can be applied. In this paper we defined throughput of the quantum network as the maximum qubits transmitted with minimum entanglement cost. Much of research work is done to improve the throughput of the quantum network using the deep learning techniques. In this paper we adopted deep learning techniques for implementing remote entanglement between two non-neighbour nodes using remote qubit teleportation and entanglement swapping. The proposed method called Optimal Remote Qubit Teleportation outperforms the throughput obtained by the state of art approach

A road towards the photonic hardware implementation of artificial cognitive circuits

Many technologies we use are inspired by nature. This happens in different domains, ranging from mechanics to optics to computer sciences. Nature has incredible potentialities that man still does not know or that he striving to learn through experience. These potentialities concern the ability to solve complex problems through approaches of various types of distributed intelligence. In fact, there are forms of intelligence in nature that differ from that of man, but are nevertheless exceedingly efficient. Man has often used as a model those forms of distributed intelligence that allow colonies of animals to develop places of housing or collective behaviors of extreme complexity. Recently, M. Alonzo et alii (Sci.Rep. 8, 5716 (2018)) published a hardware implementation to solve complex routing problems in modern information networks by exploiting the immense possibilities offered by light. This article presents an addressable photonic circuit based on the decision-making processes of ant colonies looking for food. When ants search for food, they modify their surroundings by leaving traces of pheromone, which may be reinforced and function as a type of path marker for when food has been found. This process is based on stigmergy, or the modification of the environment to implement distributed decision-making processes. The photonic hardware implementation that this work proposes is a photonic X-junction that simulates this stigmergic procedure. The experimental implementation is based on the use of non-linear substrates, i.e. materials that can be modified by light, simulating the modification induced by the ants on the surrounding environment when they leave the pheromone traces. Here, two laser beams generate two crossing channels in which the index of refraction is increased with respect to the whole substrate. These channels act as integrated waveguides (almost self-written optical fibers) within which optical information can be propagated (as happens for the ants that follow traces of pheromone already “written”). The proposed device is a X-junction with two crossing waveguides, whose refractive index contrast is defined by the intensities of the writing light beams. The higher the writing intensity, the greater the induced index variation, as if it were an increasingly intense pheromone trace. The information will follow the most contrasted harm of the junction, which is driven and eventually switched by the writing light intensity. Any optical information that will be sent to the device will follow the most intense trace, i.e. the most contrasted waveguide. The paper demonstrates a device that can be wholly operated using the light and that can be the basis of complex hardware configurations that might reproduce the stigmergic distributed intelligence. This is a highly significant innovation in the field of electronic and photonic technologies, within which artificial cognition and decision processes are implemented into a hardware circuit and not in a software code