scholarly journals The Fibonacci quantum walk and its classical trace map

2009 ◽  
Vol 388 (18) ◽  
pp. 3985-3990 ◽  
Author(s):  
A. Romanelli
Keyword(s):  
Quantum Walk ◽  
Trace Map

Totally Wild Quadratic Forms of Type E7

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Division Algebra ◽  
Quadratic Forms ◽  
Quadratic Space ◽  
Trace Map ◽  
Quaternion Division Algebra

This chapter assumes that (K, L, q) is a totally wild quadratic space of type E₇. The goal is to prove the proposition that takes into account Λ‎ of type E₇, D as the quaternion division algebra over K whose image in Br(K) is the Clifford invariant of q, and the trace and trace map. The chapter also considers two other propositions: the first states that if the trace map is not equal to zero, then the Moufang residues R₀ and R₁ are not indifferent; the second states that if the trace map is equal to zero, then the Moufang residues R₀ and R₁ are both indifferent.

Trace-map invariant and zero-energy states of the tight-binding Rudin-Shapiro model

1992 ◽  
Vol 46 (6) ◽  
pp. 3296-3304 ◽  
Author(s):  
Mihnea Dulea ◽  
Magnus Johansson ◽  
Rolf Riklund
Keyword(s):  
Tight Binding ◽  
Zero Energy ◽  
Trace Map ◽  
Energy States

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
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