scholarly journals From disordered quantum walk to physics of off-diagonal disorder

2015 ◽  
Vol 92 (21) ◽  
Author(s):  
Qifang Zhao ◽  
Jiangbin Gong
Keyword(s):  
Quantum Walk ◽  
Diagonal Disorder

scholarly journals Quantum-walk-based search algorithms with multiple marked vertices

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
G. A. Bezerra ◽  
P. H. G. Lugão ◽  
R. Portugal
Keyword(s):  
Quantum Walk ◽  
Search Algorithms

scholarly journals Bloch–Landau–Zener dynamics induced by a synthetic field in a photonic quantum walk

APL Photonics ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 020802
Author(s):  
Alessio D’Errico ◽  
Raouf Barboza ◽  
Rebeca Tudor ◽  
Alexandre Dauphin ◽  
Pietro Massignan ◽  
...  
Keyword(s):  
Quantum Walk

scholarly journals A Discontinuity of the Energy of Quantum Walk in Impurities

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1134
Author(s):  
Kenta Higuchi ◽  
Takashi Komatsu ◽  
Norio Konno ◽  
Hisashi Morioka ◽  
Etsuo Segawa
Keyword(s):  
Unit Circle ◽  
Stationary State ◽  
Discrete Time ◽  
Quantum Walk ◽  
Time Limit ◽  
The Other ◽  
Unitary Matrix ◽  
Initial State ◽  
Time Quantum ◽  
Long Time

We consider the discrete-time quantum walk whose local dynamics is denoted by a common unitary matrix C at the perturbed region {0,1,⋯,M−1} and free at the other positions. We obtain the stationary state with a bounded initial state. The initial state is set so that the perturbed region receives the inflow ωn at time n(|ω|=1). From this expression, we compute the scattering on the surface of −1 and M and also compute the quantity how quantum walker accumulates in the perturbed region; namely, the energy of the quantum walk, in the long time limit. The frequency of the initial state of the influence to the energy is symmetric on the unit circle in the complex plain. We find a discontinuity of the energy with respect to the frequency of the inflow.

scholarly journals Three-state quantum walk on the Cayley Graph of the Dihedral Group

2021 ◽  
Vol 20 (3) ◽  
Author(s):  
Ying Liu ◽  
Jia-bin Yuan ◽  
Wen-jing Dai ◽  
Dan Li
Keyword(s):  
Cayley Graph ◽  
Dihedral Group ◽  
Quantum Walk

scholarly journals Comparison of quantum-walk implementations on noisy intermediate-scale quantum computers

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
Konstantinos Georgopoulos ◽  
Clive Emary ◽  
Paolo Zuliani
Keyword(s):  
Quantum Walk ◽  
Quantum Computers ◽  
Intermediate Scale

Global Optimization With Quantum Walk Enhanced Grover Search

2014 ◽  
Author(s):  
Yan Wang
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Early Stage ◽  
Hybrid Approach ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Tunneling Effect ◽  
Grover’S Algorithm ◽  
Grover's Algorithm ◽  
Grover Search

One of the significant breakthroughs in quantum computation is Grover’s algorithm for unsorted database search. Recently, the applications of Grover’s algorithm to solve global optimization problems have been demonstrated, where unknown optimum solutions are found by iteratively improving the threshold value for the selective phase shift operator in Grover rotation. In this paper, a hybrid approach that combines continuous-time quantum walks with Grover search is proposed. By taking advantage of quantum tunneling effect, local barriers are overcome and better threshold values can be found at the early stage of search process. The new algorithm based on the formalism is demonstrated with benchmark examples of global optimization. The results between the new algorithm and the Grover search method are also compared.

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