# Efficient quantum algorithms for analyzing large sparse electrical networks

@article{Wang2017EfficientQA,
title={Efficient quantum algorithms for analyzing large sparse electrical networks},
author={Guoming Wang},
journal={Quantum Inf. Comput.},
year={2017},
volume={17},
pages={987-1026}
}
• Guoming Wang
• Published 2017
• Computer Science, Mathematics, Physics
• Quantum Inf. Comput.
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 $\operatorname{poly}(d, c, \operatorname{log}(N), 1/\lambda, 1/\epsilon… Expand 18 Citations #### Figures and Topics from this paper Linear and nonlinear quantum algorithms made explicit A thorough breakdown of common quantum algorithms into their component parts, and the explicit cost of each component in terms of fundamental quantum gates is given, and a new state-of-the-art algorithm for producing a superposition of all permutations is determined. Expand Quantum Algorithms for Systems of Linear Equations Inspired by Adiabatic Quantum Computing. • Physics, Medicine • Physical review letters • 2019 Two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state |x⟩ that is proportional to the solution of the system of linear equations Ax[over →]=b[ over →], yielding an exponential quantum speed-up under some assumptions. Expand Improved quantum backtracking algorithms through effective resistance estimates • Mathematics, Physics • ArXiv • 2017 This work presents a generalisation of one of Montanaro's algorithms to trees containing$k \geq 1$marked vertices, and achieves the conjectured bound of$\widetilde{\mathcal{O}}(\sqrt{TR_{\mathrm{max}}})$for finding a single marked vertex and k(k)(k T R R) for finding all$k$marked Vertices. Expand The Grover search as a naturally occurring phenomenon • Computer Science, Physics • Physical review letters • 2020 First evidence that under certain conditions, 1/2-spin fermions may naturally behave like a Grover search, looking for topological defects in a material is provided, hinting at novel applications of QW search. Expand An overview of quantum cellular automata • P. Arrighi • Physics, Computer Science • Natural Computing • 2019 An overview of quantum cellular automata theory is given, with particular focus on structure results; computability and universality results; and quantum simulation results. Expand Dynamical Triangulation Induced by Quantum Walk • Physics, Computer Science • Symmetry • 2020 Numerical simulations show that the number of triangles and the local curvature grow as$\alpha$and$\beta$parametrize the way geometry changes upon the local density of the walker, and that, in the long run, flatness emerges. Expand Quantum walk speedup of backtracking algorithms A general method to obtain quantum speedups of classical algorithms which are based on the technique of backtracking, a standard approach for solving constraint satisfaction problems (CSPs), and this quantum algorithm can be used to speed up the DPLL algorithm. Expand Approximate Span Programs • Mathematics, Physics • ICALP • 2016 It is shown how any span program that decides a problem$f$can also be used to decide "property testing" versions of$f, or more generally, approximate the span program witness size, a property of the input related to $f$. Expand
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