19,699 research outputs found
Riemannian-geometric entropy for measuring network complexity
A central issue of the science of complex systems is the quantitative
characterization of complexity. In the present work we address this issue by
resorting to information geometry. Actually we propose a constructive way to
associate to a - in principle any - network a differentiable object (a
Riemannian manifold) whose volume is used to define an entropy. The
effectiveness of the latter to measure networks complexity is successfully
proved through its capability of detecting a classical phase transition
occurring in both random graphs and scale--free networks, as well as of
characterizing small Exponential random graphs, Configuration Models and real
networks.Comment: 15 pages, 3 figure
A Random Walk Perspective on Hide-and-Seek Games
We investigate hide-and-seek games on complex networks using a random walk
framework. Specifically, we investigate the efficiency of various degree-biased
random walk search strategies to locate items that are randomly hidden on a
subset of vertices of a random graph. Vertices at which items are hidden in the
network are chosen at random as well, though with probabilities that may depend
on degree. We pitch various hide and seek strategies against each other, and
determine the efficiency of search strategies by computing the average number
of hidden items that a searcher will uncover in a random walk of steps. Our
analysis is based on the cavity method for finite single instances of the
problem, and generalises previous work of De Bacco et al. [1] so as to cover
degree-biased random walks. We also extend the analysis to deal with the
thermodynamic limit of infinite system size. We study a broad spectrum of
functional forms for the degree bias of both the hiding and the search strategy
and investigate the efficiency of families of search strategies for cases where
their functional form is either matched or unmatched to that of the hiding
strategy. Our results are in excellent agreement with those of numerical
simulations. We propose two simple approximations for predicting efficient
search strategies. One is based on an equilibrium analysis of the random walk
search strategy. While not exact, it produces correct orders of magnitude for
parameters characterising optimal search strategies. The second exploits the
existence of an effective drift in random walks on networks, and is expected to
be efficient in systems with low concentration of small degree nodes.Comment: 31 pages, 10 (multi-part) figure
Chebyshev expansion for Impurity Models using Matrix Product States
We improve a recently developed expansion technique for calculating real
frequency spectral functions of any one-dimensional model with short-range
interactions, by postprocessing computed Chebyshev moments with linear
prediction. This can be achieved at virtually no cost and, in sharp contrast to
existing methods based on the dampening of the moments, improves the spectral
resolution rather than lowering it. We validate the method for the exactly
solvable resonating level model and the single impurity Anderson model. It is
capable of resolving sharp Kondo resonances, as well as peaks within the
Hubbard bands when employed as an impurity solver for dynamical mean-field
theory (DMFT). Our method works at zero temperature and allows for arbitrary
discretization of the bath spectrum. It achieves similar precision as the
dynamical density matrix renormalization group (DDMRG), at lower cost. We also
propose an alternative expansion, of 1-exp(-tau H) instead of the usual H,
which opens the possibility of using established methods for the time evolution
of matrix product states to calculate spectral functions directly.Comment: 13 pages, 9 figure
Three-dimensional formation flying using bifurcating potential fields
This paper describes the design of a three-dimensional formation flying guidance and control algorithm for a swarm of autonomous Unmanned Aerial Vehicles (UAVs), using the new approach of bifurcating artificial potential fields. We consider a decentralized control methodology that can create verifiable swarming patterns, which guarantee obstacle and vehicle collision avoidance. Based on a steering and repulsive potential field the algorithm supports flight that can transition between different formation patterns by way of a simple parameter change. The algorithm is applied to linear longitudinal and lateral models of a UAV. An experimental system to demonstrate formation flying is also developed to verify the validity of the proposed control system
Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources
Proposals for near-term experiments in quantum chemistry on quantum computers
leverage the ability to target a subset of degrees of freedom containing the
essential quantum behavior, sometimes called the active space. This
approximation allows one to treat more difficult problems using fewer qubits
and lower gate depths than would otherwise be possible. However, while this
approximation captures many important qualitative features, it may leave the
results wanting in terms of absolute accuracy (basis error) of the
representation. In traditional approaches, increasing this accuracy requires
increasing the number of qubits and an appropriate increase in circuit depth as
well. Here we introduce a technique requiring no additional qubits or circuit
depth that is able to remove much of this approximation in favor of additional
measurements. The technique is constructed and analyzed theoretically, and some
numerical proof of concept calculations are shown. As an example, we show how
to achieve the accuracy of a 20 qubit representation using only 4 qubits and a
modest number of additional measurements for a simple hydrogen molecule. We
close with an outlook on the impact this technique may have on both near-term
and fault-tolerant quantum simulations
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