Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum search on the two-dimensional lattice using the staggered model
  with Hamiltonians   Quantum search on the two-dimensional lattice with one marked vertex and
cyclic boundary conditions is an important problem in the context of quantum
algorithms with an interesting unfolding. It avails to test the ability of
quantum walk models to provide efficient algorithms from the theoretical side
and means to implement quantum walks in laboratories from the practical side.
In this paper, we rigorously prove that the recent-proposed staggered quantum
walk model provides an efficient quantum search on the two-dimensional lattice,
if the reflection operators associated with the graph tessellations are used as
Hamiltonians, which is an important theoretical result for validating the
staggered model with Hamiltonians. Numerical results show that on the
two-dimensional lattice staggered models without Hamiltonians are not as
efficient as the one described in this paper and are, in fact, as slow as
classical random-walk-based algorithms.

12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin