We apply the framework of block-encodings, introduced by Low and Chuang (under the
name standard-form), to the study of quantum machine learning algorithms and derive …

This is a textbook about quantum walks and quantum search algorithms. The readers will
take advantage of the pedagogical aspects and learn the topics faster and make less effort …

Quantum algorithms can deliver asymptotic speedups over their classical counterparts.
However, there are few cases where a substantial quantum speedup has been worked out …

We describe a general method to obtain quantum speedups of classical algorithms which
are based on the technique of backtracking, a standard approach for solving constraint …

We study quantum algorithms for several fundamental string problems, including Longest
Common Substring, Lexicographically Minimal String Rotation, and Longest Square …

Branch-and-bound is a widely used technique for solving combinatorial optimization
problems where one has access to two procedures: a branching procedure that splits a set …

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

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 …

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 …

In this paper we present a quantum algorithm solving the triangle finding problem in
unweighted graphs with query complexity Õ (n 5/4), where n denotes the number of vertices …