Gaussian Amplitude Amplification for Quantum Pathfinding
Quantum Physics
2022-07-27 v3
Abstract
We study an oracle operation, along with its circuit design, which combined with the Grover diffusion operator boosts the probability of finding minimum or maximum solutions on a weighted directed graph. We focus on a geometry of sequentially connected bipartite graphs, which naturally gives rise to solution spaces describable by gaussian distributions. We then demonstrate how an oracle which encodes these distributions can be used to solve for the optimal path via amplitude amplification. And finally, we explore the degree to which this algorithm is capable of solving cases which are generated using randomized weights, as well as a theoretical application for solving the Traveling Salesman problem.
Keywords
Cite
@article{arxiv.2112.08167,
title = {Gaussian Amplitude Amplification for Quantum Pathfinding},
author = {Daniel Koch and Massimiliano Cutugno and Samuel Karlson and Saahil Patel and Laura Wessing and Paul M. Alsing},
journal= {arXiv preprint arXiv:2112.08167},
year = {2022}
}