Deterministic Quantum Search on All Laplacian Integral Graphs
AI Breakdown
Get a structured breakdown of this paper — what it's about, the core idea, and key takeaways for the field.
Abstract
Searching for an unknown marked vertex on a given graph (also known as spatial search) is an extensively discussed topic in the area of quantum algorithms, with a plethora of results based on different quantum walk models and targeting various types of graphs. Most of these algorithms have a non‐zero probability of failure. In recent years, there have been some efforts to design quantum spatial search algorithms with 100%$100\%$ success probability. However, these works either only work for very special graphs or only for the case where there is only one marked vertex. In this work, a different and elegant approach to quantum spatial search is proposed, obtaining deterministic quantum search algorithms that can find a marked vertex with certainty on any Laplacian integral graph with any predetermined proportion of marked vertices. Thus, this work discovers the largest class of graphs that allow deterministic quantum search, making it easy to design deterministic quantum search algorithms for many graphs, subsuming different graphs discussed in previous works, in a unified framework.