The effect of coherence between two photons on quantum random walk

L.J. Wang

Zijing Zhang, Feng Wang, Jie Song +1 more

In the optical quantum random walk system, phase fluctuation and beam splitter fluctuation are two unavoidable decoherence factors. These two factors degrade the performance of quantum random walk by destroying coherence, and even degrade it into a classical one. We propose a scheme for the simulation of quantum random walk using phase shifters, tunable beam splitters, and photodetectors. This proposed scheme enables us to analyze the effect of phase fluctuation and beam splitter fluctuation on two-photon quantum random walk. Furthermore, it is helpful to guide the control of phase fluctuation and beam splitter fluctuation in the experiment.

Jin-Fu Chen, Yu-Han Ma, Chang-Pu Sun

Quantum walk (QW), which is considered as the quantum counterpart of the classical random walk (CRW), is actually the quantum extension of CRW from the single-coin interpretation. The sequential unitary evolution engenders correlation between different steps in QW and leads to a non-binomial position distribution. In this paper, we propose an alternative quantum extension of CRW from the ensemble interpretation, named quantum random walk (QRW), where the walker has many unrelated coins, modeled as two-level systems, initially prepared in the same state. We calculate the walker’s position distribution in QRW for different initial coin states with the coin operator chosen as Hadamard matrix. In one-dimensional case, the walker’s position is the asymmetric binomial distribution. We further demonstrate that in QRW, coherence leads the walker to perform directional movement. For an initially decoherenced coin state, the walker’s position distribution is exactly the same as that of CRW. Moreover, we study QRW in 2D lattice, where the coherence plays a more diversified role in the walker’s position distribution.

Viv M. Kendon, Ben Tregenna

Hyunseok Jeong, Mauro Paternostro, M. S. Kim

Yunlong Su, Siyuan Liu, Xiao-Hui Wang +2 more

We investigate the behavior of coherence in scattering quantum walk search on complete graph under the condition that the total number of vertices of the graph is significantly larger than the marked number of vertices we are searching, N ≫ v. We find that the consumption of coherence represents the increase of the success probability for the searching, also it is related to the efficiency of the algorithm in oracle queries. If no coherence is consumed or an incoherent state is utilized, the algorithm will behave as the classical blind search, implying that coherence is responsible for the speed-up in this quantum algorithm over its classical counterpart. The effect of noises, in particular of photon loss and random phase shifts, on the performance of algorithm is studied. Two types of noise are considered because they arise in the optical network used for experimental realization of scattering quantum walk. It is found that photon loss will reduce the coherence and random phase shifts will hinder the interference between the edge states, both leading to lower success probability compared with the noise-free case. We then conclude that coherence plays an essential role and is responsible for the speed-up in this quantum algorithm.