Extraordinary behaviors in a two-dimensional decoherent alternative quantum walk

Chen, Tian; Zhang, Xiangdong

doi:10.1103/physreva.94.012316

Cited by 18 publications

(24 citation statements)

References 54 publications

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“…All these lattices have attracted the attention of researchers. For instance, coined quantum walks were analyzed on the two-dimensional square lattice [10][11][12][13][14][15], hexagonal lattice [16][17][18][19], and triangular lattice [19][20][21]. Since the seminal paper by Shenvi et al [22], coined quantum walks are being used for search algorithms [23].…”

Section: Introductionmentioning

confidence: 99%

Staggered quantum walk on hexagonal lattices

et al. 2018

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A discrete-time staggered quantum walk was recently introduced as a generalization that allows to unify other versions, such as the coined and Szegedy's walk. However, it also produces new forms of quantum walks not covered by previous versions. To explore their properties, we study here the staggered walk on a hexagonal lattice. Such a walk is defined using a set of overlapping tessellations that cover the graph edges, and each tessellation is a partition of the node set into cliques. The hexagonal lattice requires at least three tessellations. Each tessellation is associated with a local unitary operator and the product of the local operators defines the evolution operator of the staggered walk on the graph. After defining the evolution operator on the hexagonal lattice, we analyze the quantum walk dynamics with the focus on the position standard deviation and localization. We also obtain analytic results for the time complexity of spatial search algorithms with one marked node using cyclic boundary conditions.

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Section: Introductionmentioning

confidence: 99%

Staggered quantum walk on hexagonal lattices

et al. 2018

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“…By applying the same procedure as before, one can also find that a t out ( ) and c t 500 ( ) are always zero. Dynamics of the total system can be described with equations (16), (19), (20) and (28)- (31). In this situation, both the interactions between the atom and reservoir 1, and intracavity-external fields coupling should be taken into account.…”

Section: Lorentzian Reservoirmentioning

confidence: 99%

“…In these situations, the non-Markovian approximation involving the memory from the reservoirs should be introduced to study the dynamics of open quantum systems. Hence, the non-Markovian quantum dynamics is drawing increasing attention [28][29][30][31][32][33][34][35][36][37][38][39][40][41].Here, in a non-Markovian approach, we investigate the performance of a quantum controlled-PHASE gate constituted by an atom trapped in a single-sided cavity. Both the coupling between an atom and the environment and the interaction between the single cavity mode and a reservoir are taken into account.…”

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confidence: 99%

Deterministic quantum controlled-PHASE gates based on non-Markovian environments

2017

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We study the realization of the quantum controlled-PHASE gate in an atom-cavity system beyond the Markovian approximation. The general description of the dynamics for the atom-cavity system without any approximation is presented. When the spectral density of the reservoir has the Lorentz form, by making use of the memory backflow from the reservoir, we can always construct the deterministic quantum controlled-PHASE gate between a photon and an atom, no matter the atomcavity coupling strength is weak or strong. While, the phase shift in the output pulse hinders the implementation of quantum controlled-PHASE gates in the sub-Ohmic, Ohmic or super-Ohmic reservoirs.

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“…Quantum information exhibits the advantage over its classical counterpart due to the appearance of the quantum speedup [1][2][3][4][5][6][7][8][9][10][11][12]. Long-lived quantum speedup has been widely applied in the quantum information processing, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…One ideal theoretical scheme involving the long-lived quantum speedup is the quantum walk [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In the quantum walk [2][3][4][5][6][7][8][9][10][11][12][13][14][15], a walker initially located at one site of a graph has a probability of reaching two adjacent sites, and then reaches each site of the graph as time passes. The walker's state is described by a superposition of positions in the quantum walk, which is different from a probability distribution over positions in the classical walk [3,4].…”

Section: Introductionmentioning

confidence: 99%

Long-lived quantum speedup based on plasmonic hot spot systems

2019

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Long-lived quantum speedup serves as a fundamental component for quantum algorithms. The quantum walk is identified as an ideal scheme to realize the long-lived quantum speedup. However, one finds that the duration of quantum speedup is too short in real systems to implement the quantum algorithms, for instance the speedup in the photosynthetic light-harvesting systems can last only dozens of femtoseconds. Here, we construct one plasmonic system with two-level molecules embodied in the hot spots of one-dimensional nanoparticle chains to realize the long-lived quantum speedup. The coherent and incoherent coupling parameters in the system are obtained by means of Green's tensor technique. Our results reveal that the duration of quantum speedup in our scheme can exceed 500 fs under strong coherent coupling conditions. Moreover, our plasmonic system has far prospect in realizing high-dimensional quantum walk, which is very beneficial for quantum algorithms.

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Extraordinary behaviors in a two-dimensional decoherent alternative quantum walk

Cited by 18 publications

References 54 publications

Staggered quantum walk on hexagonal lattices

Staggered quantum walk on hexagonal lattices

Deterministic quantum controlled-PHASE gates based on non-Markovian environments

Long-lived quantum speedup based on plasmonic hot spot systems

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