Quantum Speedup for Graph Sparsification, Cut Approximation and Laplacian Solving

Explore quantum algorithms for graph sparsification, cut approximation, and Laplacian solving in this 25-minute IEEE conference talk. Delve into the contributions of Simon Apers and Ronald de Wolf as they present their research on quantum speedup for these graph-related problems. Learn about classical sparsification algorithms, quantum spanner algorithms, and quantum sparsification algorithms. Discover the innovative bootstrapping trick and matching quantum lower bound. Gain insights into cut approximation and Laplacian solving techniques, and understand how quantum computing can potentially accelerate these graph algorithms.

Intro
Graph Sparsification
Spectral Sparsification
Our Contribution
Classical Sparsification Algorithm
Quantum Spanner Algorithm
Quantum Sparsification Algorithm
A Bootstrapping Trick
Matching Quantum Lower Bound
Cut Approximation
Laplacian Solving