Decoherence in a one-dimensional quantum walk

@article{Annabestani2010DecoherenceIA,
  title={Decoherence in a one-dimensional quantum walk},
  author={Mostafa Annabestani and Seyed Javad Akhtarshenas and Mohamad Reza Abolhassani},
  journal={Physical Review A},
  year={2010},
  volume={81},
  pages={032321}
}
In this article we study decoherence in the discrete-time quantum walk on the line. We generalize the method of decoherent coin quantum walk, introduced by Brun et al. [Phys. Rev. A 67, 32304 (2003)]. Our analytical expressions are applicable for all kinds of decoherence. As an example of the coin-position decoherence, we study the broken line quantum walk and compare our results with the numerical one. We also show that our analytical results reduce to the Brun formalism when only the coin is… 

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References

SHOWING 1-10 OF 52 REFERENCES
Decoherence in Discrete Quantum Walks
We present an introduction to coined quantum walks on regular graphs, which have been developed in the past few years as an alternative to quantum Fourier transforms for underpinning algorithms for
Quantum Walks on the Hypercube
TLDR
Two quantum walks on the n-dimensional hypercube are studied, one in discrete time and one in continuous time, showing that the instantaneous mixing time is (π/4)n steps, faster than the Θ(n log n) steps required by the classical walk.
Quantum computation and quantum information
  • T. Paul
  • Mathematics, Computer Science
    Mathematical Structures in Computer Science
  • 2007
This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers deal
Quantum Walks for Computer Scientists
TLDR
The purpose of this lecture is to provide a concise yet comprehensive introduction to quantum walks, an emerging field of quantum computation, is a generalization of random walks into the quantum mechanical world.
Quantum Potential Theory
Potential Theory in Classical Probability.- to Random Walks on Noncommutative Spaces.- Interactions between Quantum Probability and Operator Space Theory.- Dirichlet Forms on Noncommutative Spaces.-
Physica A 347
  • 137
  • 2004
Phys
  • Rev. A 67, 032304
  • 2003
I and J
A: Math
  • Theor. 43, 075301
  • 2010
SIGACT News 35
  • 22 (2004). 032321-8 DECOHERENCE IN A ONE-DIMENSIONAL QUANTUM WALK PHYSICAL REVIEW A 81, 032321
  • 2010
...
1
2
3
4
5
...