Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improving the query complexity of quantum spatial search in two
  dimensions   The question of whether quantum spatial search in two dimensions can be made
optimal has long been an open problem. We report progress towards its
resolution by showing that the oracle complexity for target location can be
made optimal, by increasing the number of calls to the walk operator that
incorporates the graph structure by a logarithmic factor. Our algorithm does
not require amplitude amplification. An important ingredient of our algorithm
is the implementation of multi-step quantum walks by graph powering, using a
coin space of walk-length dependent dimension, which may be of independent
interest. Finally, we demonstrate how to implement quantum walks arising from
powers of symmetric Markov chains using our methods.

22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph