Quantum walks and quantum search on graphene lattices
@article{Foulger2015QuantumWA, title={Quantum walks and quantum search on graphene lattices}, author={Iain Foulger and Sven Gnutzmann and Gregor Tanner}, journal={Physical Review A}, year={2015}, volume={91}, pages={062323}, url={https://api.semanticscholar.org/CorpusID:118480006} }
This work describes how the need for extra degrees of freedom can be negated by utilising a graphene lattice, demonstrating that a continuous-time quantum search in the experimentally relevant regime of two-dimensions is possible and demonstrates the feasibility of realising the quantum search and transfer mechanisms on graphene.
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88 References
Quantum Walks and Search Algorithms
- 2013
Computer Science, Physics
The reader will benefit from the pedagogical aspects of the book, learning faster and with more ease than would be possible from the primary research literature, and guidelines for the use of computer programs to simulate the evolution of quantum walks are provided.
Quantum Walk in Position Space with Single Optically Trapped Atoms
- 2009
Physics
In this experiment, a quantum walk on the line with single neutral atoms is implemented by deterministically delocalizing them over the sites of a one-dimensional spin-dependent optical lattice and its spatial coherence is demonstrated.
Under consideration for publication in Math. Struct. in Comp. Science Decoherence in quantum walks- a review
- 2006
Physics, Computer Science
Microwave experiments simulating quantum search and directed transport in artificial graphene.
- 2015
Physics
A proof of principle experiment implementing wave search algorithms and directed wave transport in a graphene lattice arrangement based on bringing localized search states into resonance with an extended lattice state in an energy region of low spectral density at or near the Dirac point.
Quantum walks: a comprehensive review
- 2012
Physics, Computer Science
This paper has reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.
Alternate two-dimensional quantum walk with a single-qubit coin
- 2011
Physics
We have recently proposed a two-dimensional quantum walk where the requirement of a higher dimensionality of the coin space is substituted with the alternance of the directions in which the walker…
Experimental realization of a delayed-choice quantum walk
- 2013
Physics
This is the first experiment realizing a multi-dimensional quantum walk with a single photon source and the first experimental simulation of the Grover walk, a model that can be used to implement theGrover quantum search algorithm.
Spatial search by continuous-time quantum walks on crystal lattices
- 2014
Physics, Computer Science
By constructing lattice Hamiltonians exhibiting Dirac points in their dispersion relations and exploiting the linear behavior near a Dirac point, this work develops algorithms that solve the problem of searching a general $d$-dimensional lattice of $N$ vertices for a single marked item using a continuous-time quantum walk in a time of $O(\sqrt{N})$.
Realization of quantum walks with negligible decoherence in waveguide lattices.
- 2008
Physics
It is shown that the propagation of photons in waveguide lattices, which have been studied extensively in recent years, are essentially an implementation of quantum walks.
One-dimensional quantum walks
- 2001
Physics, Computer Science
A quantum analog of the symmetric random walk, which the authors call the Hadamard walk, is analyzed, which has position that is nearly uniformly distributed in the range after steps, in sharp contrast to the classical random walk.