Quadratic Speedup for Finding Marked Vertices by Quantum Walks

Explore a quantum algorithm that achieves quadratic speedup in finding marked vertices using quantum walks. Delve into the comparison between exhaustive search, structured search, and search by random walk methods. Examine constraints and applications of this approach, including Szegedy's 2004 work on detecting and finding marked elements. Analyze the original, absorbing, and interpolated walks, as well as quantum fast-forwarding techniques. Investigate the connection to classical walks and gain insights into the final results of this quantum speedup algorithm.

Intro
Exhaustive search
Structured search
Search by random walk
Constraints
Applications
Szegedy'04
Detecting marked elements
Finding marked elements
Original walk
Absorbing walk
Interpolated walk
Quantum fast-forwarding
Our result
Connection to the classical walk
Analysis of classical walk
Final result