scholarly journals Qubit state transfer via discrete-time quantum walks

2015 ◽  
Vol 48 (22) ◽  
pp. 225302 ◽  
Author(s):  
İskender Yalçınkaya ◽  
Zafer Gedik
Keyword(s):  
Discrete Time ◽  
Quantum Walks ◽  
Qubit State ◽  
State Transfer ◽  
Time Quantum

scholarly journals Periodicity and perfect state transfer in quantum walks on variants of cycles

2014 ◽  
Vol 14 (5&6) ◽  
pp. 417-438
Author(s):  
Katharine E. Barr ◽  
Tim J. Proctor ◽  
Daniel Allen ◽  
Viv M. Kendon
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
Quantum Walks ◽  
High Fidelity ◽  
Perfect State ◽  
Initial State ◽  
State Transfer ◽  
Time Quantum ◽  
Perfect State Transfer ◽  
Very High

We systematically investigated perfect state transfer between antipodal nodes of discrete time quantum walks on variants of the cycles $C_4$, $C_6$ and $C_8$ for three choices of coin operator. Perfect state transfer was found, in general, to be very rare, only being preserved for a very small number of ways of modifying the cycles. We observed that some of our useful modifications of $C_4$ could be generalised to an arbitrary number of nodes, and present three families of graphs which admit quantum walks with interesting dynamics either in the continuous time walk, or in the discrete time walk for appropriate selections of coin and initial conditions. These dynamics are either periodicity, perfect state transfer, or very high fidelity state transfer. These families are modifications of families known not to exhibit periodicity or perfect state transfer in general. The robustness of the dynamics is tested by varying the initial state, interpolating between structures and by adding decoherence.

Generalized teleportation by means of discrete-time quantum walks on N-lines and N-cycles

2019 ◽  
Vol 33 (06) ◽  
pp. 1950070 ◽  
Author(s):  
Yu-Guang Yang ◽  
Sheng-Nan Cao ◽  
Wei-Feng Cao ◽  
Dan Li ◽  
Yi-Hua Zhou ◽  
...  
Keyword(s):  
Quantum Entanglement ◽  
Discrete Time ◽  
Quantum Teleportation ◽  
Quantum Communication ◽  
Communication Protocols ◽  
Quantum Walks ◽  
Qubit State ◽  
Time Quantum ◽  
Open Question

Recently, Wang et al. [Wang et al., Quantum Inf. Process. 16 (2017) 221] developed generalized teleportation schemes based on different quantum walks structures. In their paper, an interesting open question is whether there are other graphs suitable for teleportation. Here, we extend the results of quantum teleportation of an unknown qubit state by means of discrete-time quantum walks and propose two kinds of schemes for quantum teleportation by means of discrete-time quantum walks on N-lines and N-cycles, respectively. Likewise, prior quantum entanglement is unnecessary for teleportation and quantum entanglement is generated by means of quantum walks. This further opens wider applications of quantum walks in quantum communication protocols.

scholarly journals Discrete-time quantum walks generated by aperiodic fractal sequence of space coin operators

2018 ◽  
Vol 29 (10) ◽  
pp. 1850098 ◽  
Author(s):  
R. F. S. Andrade ◽  
A. M. C. Souza
Keyword(s):  
Wave Function ◽  
Probability Distribution ◽  
Discrete Time ◽  
Numerical Study ◽  
Entanglement Entropy ◽  
Quantum Effects ◽  
Quantum Walks ◽  
Cantor Set ◽  
One Dimensional ◽  
Time Quantum

Properties of one-dimensional discrete-time quantum walks (DTQWs) are sensitive to the presence of inhomogeneities in the substrate, which can be generated by defining position-dependent coin operators. Deterministic aperiodic sequences of two or more symbols provide ideal environments where these properties can be explored in a controlled way. Based on an exhaustive numerical study, this work discusses a two-coin model resulting from the construction rules that lead to the usual fractal Cantor set. Although the fraction of the less frequent coin [Formula: see text] as the size of the chain is increased, it leaves peculiar properties in the walker dynamics. They are characterized by the wave function, from which results for the probability distribution and its variance, as well as the entanglement entropy, were obtained. A number of results for different choices of the two coins are presented. The entanglement entropy has shown to be very sensitive to uncovering subtle quantum effects present in the model.

scholarly journals Dynamics and energy spectra of aperiodic discrete-time quantum walks

2017 ◽  
Vol 96 (1) ◽  
Author(s):  
N. Lo Gullo ◽  
C. V. Ambarish ◽  
Th. Busch ◽  
L. Dell'Anna ◽  
C. M. Chandrashekar
Keyword(s):  
Discrete Time ◽  
Quantum Walks ◽  
Energy Spectra ◽  
Time Quantum

The non-uniform stationary measure for discrete-time quantum walks in one dimension

2015 ◽  
Vol 15 (11&12) ◽  
pp. 1060-1075
Author(s):  
Norio Konno ◽  
Masato Takei
Keyword(s):  
Eigenvalue Problem ◽  
Discrete Time ◽  
Quantum Walks ◽  
Stationary Measure ◽  
Unitary Matrix ◽  
Uniform Measure ◽  
Simple Argument ◽  
Stationary Measures ◽  
Time Quantum ◽  
The One

We consider stationary measures of the one-dimensional discrete-time quantum walks (QWs) with two chiralities, which is defined by a 2 $\times$ 2 unitary matrix $U$. In our previous paper \cite{Konno2014}, we proved that any uniform measure becomes the stationary measure of the QW by solving the corresponding eigenvalue problem. This paper reports that non-uniform measures are also stationary measures of the QW except when $U$ is diagonal. For diagonal matrices, we show that any stationary measure is uniform. Moreover, we prove that any uniform measure becomes a stationary measure for more general QWs not by solving the eigenvalue problem but by a simple argument.

Photonic discrete-time quantum walks [Invited]

2020 ◽  
Vol 18 (5) ◽  
pp. 052701
Author(s):  
Gaoyan Zhu ◽  
Lei Xiao ◽  
Bingzi Huo ◽  
Peng Xue
Keyword(s):  
Discrete Time ◽  
Quantum Walks ◽  
Time Quantum
Sign in / Sign up

Export Citation Format

Share Document