Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Search via Quantum Walk   We propose a new method for designing quantum search algorithms for finding a
"marked" element in the state space of a classical Markov chain. The algorithm
is based on a quantum walk \'a la Szegedy (2004) that is defined in terms of
the Markov chain. The main new idea is to apply quantum phase estimation to the
quantum walk in order to implement an approximate reflection operator. This
operator is then used in an amplitude amplification scheme. As a result we
considerably expand the scope of the previous approaches of Ambainis (2004) and
Szegedy (2004). Our algorithm combines the benefits of these approaches in
terms of being able to find marked elements, incurring the smaller cost of the
two, and being applicable to a larger class of Markov chains. In addition, it
is conceptually simple and avoids some technical difficulties in the previous
analyses of several algorithms based on quantum walk.

11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys