Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Experimental parity-time symmetry quantum walks on a directed graph   Quantum walks (QW) are of crucial importance in the development of quantum
information processing algorithms. Recently, several quantum algorithms have
been proposed to implement network analysis, in particular to rank the
centrality of nodes in networks represented by graphs. Employing QW in
centrality ranking is advantageous comparing to certain widely used classical
algorithms (e.g. PageRank) because QW approach can lift the vertex rank
degeneracy in certain graphs. However, it is challenging to implement a
directed graph via QW, since it corresponds to a non-Hermitian Hamiltonian and
thus cannot be accomplished by conventional QW. Here we report the realizations
of centrality rankings of both a three-vertex and four-vertex directed graphs
with parity-time (PT) symmetric quantum walks. To achieve this, we use
high-dimensional photonic quantum states, optical circuitries consisting of
multiple concatenated interferometers and dimension dependent loss.
Importantly, we demonstrate the advantage of QW approach experimentally by
breaking the vertex rank degeneracy in a four-vertex graph. Our work shows that
PT-symmetric quantum walks may be useful for realizing advanced algorithm in a
quantum network.

4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph