



01309nas a2200133   4500008004100000245008000041210006900121260001500190300001300205490000700218520089600225100001801121856003601139       2017                        eng d00aEfficient quantum algorithms for analyzing large sparse electrical networks0 aEfficient quantum algorithms for analyzing large sparse electric  c2017/07/21  a987-10260 v173 a<p>Analyzing large sparse electrical networks is a fundamental task in physics, electrical engineering and computer science. We propose two classes of quantum algorithms for this task. The first class is based on solving linear systems, and the second class is based on using quantum walks. These algorithms compute various electrical quantities, including voltages, currents, dissipated powers and effective resistances, in time poly(d, c,log(N),1/λ,1/ε), where N is the number of vertices in the network, d is the maximum unweighted degree of the vertices, c is the ratio of largest to smallest edge resistance, λ is the spectral gap of the normalized Laplacian of the network, and ε is the accuracy. Furthermore, we show that the polynomial dependence on 1/λ is necessary. This implies that our algorithms are optimal up to polynomial factors and cannot be signficantly improved.</p>1 aWang, Guoming  uhttps://arxiv.org/abs/1311.1851