Finding a good approximation of the top eigenvector of a given $ d\times d $ matrix $ A $ is a
basic and important computational problem, with many applications. We give two different …

The edge list model is arguably the simplest input model for graphs, where the graph is
specified by a list of its edges. In this model, we study the quantum query complexity of three …

Grover's algorithm leverages quantum computing to efficiently locate solutions in
unstructured search spaces, outperforming classical approaches. Since Grover's algorithm …

This thesis is concerned with scaling problems, which have been of much interest in recent
years. It is a class of computational problems with a plethora of connections to different …

Optimization is the process of selecting the best option from all possibilities, and problems
related to finding the best option among many options are called optimization problems. A …

The goal of graph sparsification is to compress large graphs into smaller ones. In vertex
sparsification we are given a graph and a set of terminals. We aim to find a graph with the …