scholarly journals Entanglement and interaction in a topological quantum walk

2018 ◽  
Vol 5 (2) ◽  
Author(s):  
Alberto Verga ◽  
Ricardo Gabriel Elias
Keyword(s):  
Quantum Walk ◽  
Edge State ◽  
Interacting Particles ◽  
Topological Quantum

We study the quantum walk of two interacting particles on a line with an interface separating two topologically distinct regions. The interaction induces a localization-delocalization transition of the edge state at the interface. We characterize the transition through the entanglement between the two particles.

scholarly journals Topological quantum walk with discrete time-glide symmetry

2020 ◽  
Vol 102 (3) ◽  
Author(s):  
Ken Mochizuki ◽  
Takumi Bessho ◽  
Masatoshi Sato ◽  
Hideaki Obuse
Keyword(s):  
Discrete Time ◽  
Quantum Walk ◽  
Topological Quantum

scholarly journals Edge-state-enhanced transport in a two-dimensional quantum walk

2015 ◽  
Vol 91 (2) ◽  
Author(s):  
Janos K. Asboth ◽  
Jonathan M. Edge
Keyword(s):  
Quantum Walk ◽  
Edge State ◽  
Two Dimensional

Linear AC transport in T-stub and crossed silicene nanosystems

2018 ◽  
Vol 32 (03) ◽  
pp. 1850016
Author(s):  
Yun-Lei Sun ◽  
En-Jia Ye
Keyword(s):  
Electric Field ◽  
Transport Properties ◽  
External Electric Field ◽  
Nearest Neighbor ◽  
Transport Theory ◽  
Energy Gap ◽  
Local Density ◽  
Tight Binding ◽  
Edge State ◽  
Topological Quantum

In this work, we theoretically study the linear AC transport properties in T-stub and crossed zigzag silicene nanosystems. The DC conductance and AC emittance are numerically calculated based on the tight-binding approach and AC transport theory, by considering the nearest-neighbor hopping, second-nearest-neighbor spin-orbit interaction (SOI) and external electric field. The relatively strong SOI of silicene was demonstrated to induce a topological quantum edge state in the nanosystems by the local density of states, which eliminates the AC emittance response at the Dirac point. Further investigations suggest that the SOI-induced AC transport is topologically protected from the changes of geometrical size. Moreover, the AC transport properties of these nanosystems can be tuned by the external electric field, which would open an energy gap and destroy the topological quantum state, making them trivial band insulators.

scholarly journals Statistical moments of quantum-walk dynamics reveal topological quantum transitions

2016 ◽  
Vol 7 (1) ◽  
Author(s):  
Filippo Cardano ◽  
Maria Maffei ◽  
Francesco Massa ◽  
Bruno Piccirillo ◽  
Corrado de Lisio ◽  
...  
Keyword(s):  
Quantum Walk ◽  
Statistical Moments ◽  
Topological Quantum ◽  
Quantum Transitions

scholarly journals Borromean states in discrete-time quantum walks

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 523
Author(s):  
Marcin Markiewicz ◽  
Marcin Karczewski ◽  
Pawel Kurzynski
Keyword(s):  
Discrete Time ◽  
Bound States ◽  
Quantum Walk ◽  
Bound State ◽  
Quantum Walks ◽  
Interacting Particles ◽  
Time Quantum ◽  
The Right ◽  
Efimov States ◽  
Peculiar Behavior

In the right conditions, removing one particle from a multipartite bound state can make it fall apart. This feature, known as the "Borromean property", has been recently demonstrated experimentally in Efimov states. One could expect that such peculiar behavior should be linked with the presence of strong inter-particle correlations. However, any exploration of this connection is hindered by the complexity of the physical systems exhibiting the Borromean property. To overcome this problem, we introduce a simple dynamical toy model based on a discrete-time quantum walk of many interacting particles. We show that the particles described by it need to exhibit the Greenberger-Horne-Zeillinger (GHZ) entanglement to form Borromean bound states. As this type of entanglement is very prone to particle losses, our work demonstrates an intuitive link between correlations and Borromean properties of the system. Moreover, we discuss our findings in the context of the formation of composite particles.

scholarly journals Topological quantum computation based on chiral Majorana fermions

2018 ◽  
Vol 115 (43) ◽  
pp. 10938-10942 ◽  
Author(s):  
Biao Lian ◽  
Xiao-Qi Sun ◽  
Abolhassan Vaezi ◽  
Xiao-Liang Qi ◽  
Shou-Cheng Zhang
Keyword(s):  
Quantum Computation ◽  
Edge State ◽  
Majorana Fermion ◽  
Majorana Fermions ◽  
Hybrid Device ◽  
Topological Quantum ◽  
Ring Junction ◽  
Phase Gate ◽  
Topological Quantum Computation ◽  
Junction Conductance

The chiral Majorana fermion is a massless self-conjugate fermion which can arise as the edge state of certain 2D topological matters. It has been theoretically predicted and experimentally observed in a hybrid device of a quantum anomalous Hall insulator and a conventional superconductor. Its closely related cousin, the Majorana zero mode in the bulk of the corresponding topological matter, is known to be applicable in topological quantum computations. Here we show that the propagation of chiral Majorana fermions leads to the same unitary transformation as that in the braiding of Majorana zero modes and propose a platform to perform quantum computation with chiral Majorana fermions. A Corbino ring junction of the hybrid device can use quantum coherent chiral Majorana fermions to implement the Hadamard gate and the phase gate, and the junction conductance yields a natural readout for the qubit state.

Topological quantum scheme based on quantum walk

2007 ◽  
Author(s):  
Andis C. T. Kwan ◽  
Xiangdong Li ◽  
Lin Leung ◽  
Michael Anshel
Keyword(s):  
Quantum Walk ◽  
Topological Quantum

Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Dimensional Space ◽  
Space Time ◽  
Elementary Particles ◽  
Hierarchy Problem ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
New Formula

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

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