Experimental Quantum Fast Hitting on Hexagonal Graphs

Nature Photonics, 12, 754-758 (2018)


Quantum walks are powerful kernels in quantum computing protocols, and possess strong capabilities in speeding up various simulation and optimization tasks. One striking example is provided by quantum walkers evolving on glued trees1, which demonstrate faster hitting performances than classical random walks. However, their experimental implementation is challenging, as this involves highly complex arrangements of an exponentially increasing number of nodes. Here, we propose an alternative structure with a polynomially increasing number of nodes. We successfully map such graphs on quantum photonic chips using femtosecond-laser direct writing techniques in a geometrically scalable fashion. We experimentally demonstrate quantum fast hitting by implementing two-dimensional quantum walks on graphs with up to 160 nodes and a depth of eight layers, achieving a linear relationship between the optimal hitting time and the network depth. Our results open up a scalable path towards quantum speedup in classically intractable complex problems.


Hao Tang
Carlo Di Franco
Zi-Yu Shi
Tian-Shen He
Zhen Feng
Jun Gao
Ke Sun
Zhan-Ming Li
Zhi-Qiang Jiao
Tian-Yu Wang
M. S. Kim
Xian-Min Jin


The paper is available at https://www.nature.com/articles/s41566-018-0282-5.