Concrete resource analysis of the quantum linear system algorithm used to compute the electromagnetic scattering cross section of a 2D target

We provide a detailed estimate for the logical resource requirements of the quantum linear system algorithm (QLSA) [Phys. Rev. Lett. 103, 150502 (2009)] including the recently described elaborations [Phys. Rev. Lett. 110, 250504 (2013)]. Our resource estimates are based on the standard quantum-circuit model of quantum computation; they comprise circuit width, circuit depth, the number of qubits and ancilla qubits employed, and the overall number of elementary quantum gate operations as well as more specific gate counts for each elementary fault-tolerant gate from the standard set {X, Y, Z, H, S, T, CNOT}. To perform these estimates, we used an approach that combines manual analysis with automated estimates generated via the Quipper quantum programming language and compiler. Our estimates pertain to the example problem size N=332,020,680 beyond which, according to a crude big-O complexity comparison, QLSA is expected to run faster than the best known classical linear-system solving algorithm. For this problem size, a desired calculation accuracy 0.01 requires an approximate circuit width 340 and circuit depth of order $10^{25}$ if oracle costs are excluded, and a circuit width and depth of order $10^8$ and $10^{29}$, respectively, if oracle costs are included, indicating that the commonly ignored oracle resources are considerable. In addition to providing detailed logical resource estimates, it is also the purpose of this paper to demonstrate explicitly how these impressively large numbers arise with an actual circuit implementation of a quantum algorithm. While our estimates may prove to be conservative as more efficient advanced quantum-computation techniques are developed, they nevertheless provide a valid baseline for research targeting a reduction of the resource requirements, implying that a reduction by many orders of magnitude is necessary for the algorithm to become practical.Comment: 37 pages, 40 figure

Stacking Entropy of Hard Sphere Crystals

Classical hard spheres crystallize at equilibrium at high enough density. Crystals made up of stackings of 2-dimensional hexagonal close-packed layers (e.g. fcc, hcp, etc.) differ in entropy by only about $10^{-3}k_B$ per sphere (all configurations are degenerate in energy). To readily resolve and study these small entropy differences, we have implemented two different multicanonical Monte Carlo algorithms that allow direct equilibration between crystals with different stacking sequences. Recent work had demonstrated that the fcc stacking has higher entropy than the hcp stacking. We have studied other stackings to demonstrate that the fcc stacking does indeed have the highest entropy of ALL possible stackings. The entropic interactions we could detect involve three, four and (although with less statistical certainty) five consecutive layers of spheres. These interlayer entropic interactions fall off in strength with increasing distance, as expected; this fall-off appears to be much slower near the melting density than at the maximum (close-packing) density. At maximum density the entropy difference between fcc and hcp stackings is $0.00115 +/- 0.00004 k_B$ per sphere, which is roughly 30% higher than the same quantity measured near the melting transition.Comment: 15 page

EXPLOITING DATA DIVERSITY AND MULTIUSER DIVERSITY IN NONCOOPERATIVE MOBILE INFOSTATION NETWORKS

Abstract — In wireless networks, it is often assumed that nodes cooperate to relay packets for one another. Although this is a plausible model for military or mission based networks, it is unrealistic for commercial networks and future pervasive computing environments. We address the issue of noncooperation between nodes in the context of content distribution in mobile infostation networks. We assume all nodes have common interest in all files cached in the fixed infostations. In addition to downloading files from the fixed infostations, nodes act as mobile infostations and exchange files when they are in proximity. We stipulate a social contract such that an exchange takes place only when each node can obtain something it wants from the exchange. Our social contract opportunistically aligns the individual node’s interest with that of the whole distribution network and hence enables much higher system efficiency compared to downloading only from fixed infostations while not requiring true cooperation among nodes. We show by analysis and simulations that network performance depends on the node density, mobility and the number of files that are being disseminated. Our results point to the existence of data diversity for mobile infostation networks. The achievable throughput increases as the number of files of interest to all users increases. We have also extended the common interest model to the case where nodes have dissimilar interests. Our simulation results show that as mobile nodes change from having identical interests to mutually exclusive interests, the network performance degrades dramatically. We propose an alternate user strategy when nodes have partially overlapping interests and show that the network throughput can be significantly improved by exploiting multiuser diversity inherent in mobile infostation networks. We conclude that data diversity and multiuser diversity exist in noncooperative mobile infostation networks and can be exploited. 1

Joint Network-Centric and User-Centric Radio Resource Management In . . .

A pricing mechanism to mediate (and allocate resources) between conflicting user and network objectives has been recently proposed [1] in a single-cell system. Here, we extend the results to a multicell system where the autonomous base station assignment and power control are formulated as a non-cooperative game among users. The network prices the resources using two strategies: global pricing that maximizes the revenue and minimax pricing that trades off the revenue for an evener resource allocation

Joint network-centric and user-centric radio resource management in a multicell system

Abstract A pricing mechanism to mediate (and allocate resources) between conflicting user and network objectives has been recently proposed Index Terms Power Control, Pricing, Utility, Radio Resource Management, Revenue Maximization I. INTRODUCTION Pricing, and more generally microeconomic principles, have recently emerged as powerful tools for resource allocation in wireless networks In this paper, we extend the work in [1, 2] for a single-cell system to a multicell system. Each individual user has to adjust its transmitter power based on the base station it is assigned to. Different base station assignments will lead to different power control results. In this paper, we let the user choose the base station where the user's net utility is maximized. Therefore, the power control and base station assignment are integrated in the user-centric optimization. For the network-centric optimization, we apply two approaches: one is global pricing where the network seeks a unit price for global revenue maximization and the other is minimax pricing where a unit price is assigned based on maximizing the revenue at the base station with the smallest local optimum unit price. The paper is organized as follows. In Section II, we define in a multicell CDMA system the user metric (utility function) and the network metric (revenue) as well as the pricing (or payment) function that mediates between the user objectives and the network objective. We present in Section III our joint user-centric and network-centric optimization problems. Our numerical results are presented in Section IV

NONCOOPERATIVE CONTENT DISTRIBUTION IN MOBILE INFOSTATION NETWORKS

Abstract — In wireless networks, it is often assumed that all nodes cooperate to relay packets for each other. Although this is a plausible model for military or mission based networks, it is unrealistic for commercial networks and future pervasive computing environments. We address the issue of noncooperation between nodes in the context of content distribution in mobile infostation networks. All nodes have common interest in all files cached in the fixed infostations. In addition to downloading files from the fixed infostations, nodes act as mobile infostations and exchange files when they are in proximity. We stipulate a social contract such that an exchange occurs only when each node can obtain something it wants from the exchange. We show by analysis and simulations that network performance depends on node density, mobility and the number of files that are being disseminated. Our results point to the existence of data diversity for mobile infostation networks. As the number of files of interest to all users increases, the achievable throughput increases. Moreover, each user has a more fair share of the total network throughput. In particular, when the number of files of shared interest is large, the transmission of each channel is only limited by contention, indicating the noncooperation strategy achieves near optimum resource utilization. I