Quantum computers are expected to surpass the computational capabilities of classical
computers during this decade and have transformative impact on numerous industry sectors …

Continuous-time quantum walks provide a natural framework to tackle the fundamental
problem of finding a node among a set of marked nodes in a graph, known as spatial …

The main results on quantum walk search are scattered over different, incomparable
frameworks, most notably the hitting time framework, originally by Szegedy, the electric …

We develop three new methods to implement any Linear Combination of Unitaries (LCU), a
powerful quantum algorithmic tool with diverse applications. While the standard LCU …

While the quantum query complexity of k-distinctness is known to be O (n 3/4− 1/4 (2 k− 1))
for any constant k≥ 4 [Belovs, FOCS 2012], the best previous upper bound on the time …

The quantum walk is a powerful tool to develop quantum algorithms, which usually are
based on searching for a vertex in a graph with multiple marked vertices, with Ambainis's …

There has been a very large body of research on searching a marked vertex on a graph
based on quantum walks, and Grover's algorithm can be regarded as a quantum walk …

Quantum walk is widely used in search problems, and it has an ideal acceleration effect
compared with classical algorithm. Suppose there is a marked vertex w on Johnson graph J …

One of the most important algorithmic applications of quantum walks is to solve spatial
search problems. A widely used quantum algorithm for this problem, introduced by Childs …

Quantum walk is the quantum version of classical random walk, which has shown great
advantage over classical algorithms. In this article, main discoveries and breakthroughs …