3,168 research outputs found
Coined quantum walks on percolation graphs
Quantum walks, both discrete (coined) and continuous time, form the basis of
several quantum algorithms and have been used to model processes such as
transport in spin chains and quantum chemistry. The enhanced spreading and
mixing properties of quantum walks compared with their classical counterparts
have been well-studied on regular structures and also shown to be sensitive to
defects and imperfections in the lattice. As a simple example of a disordered
system, we consider percolation lattices, in which edges or sites are randomly
missing, interrupting the progress of the quantum walk. We use numerical
simulation to study the properties of coined quantum walks on these percolation
lattices in one and two dimensions. In one dimension (the line) we introduce a
simple notion of quantum tunneling and determine how this affects the
properties of the quantum walk as it spreads. On two-dimensional percolation
lattices, we show how the spreading rate varies from linear in the number of
steps down to zero, as the percolation probability decreases to the critical
point. This provides an example of fractional scaling in quantum walk dynamics.Comment: 25 pages, 14 figures; v2 expanded and improved presentation after
referee comments, added extra figur
Experimental realization of a momentum-space quantum walk
We report on a discrete-time quantum walk that uses the momentum of
ultra-cold rubidium-87 atoms as the walk space and two internal atomic states
as the coin degree of freedom. Each step of the walk consists of a coin toss (a
microwave pulse) followed by a unitary shift operator (a resonant ratchet
pulse). We carry out a comprehensive experimental study on the effects of
various parameters, including the strength of the shift operation, coin
parameters, noise, and initialization of the system on the behavior of the
walk. The walk dynamics can be well controlled in our experiment; potential
applications include atom interferometry and engineering asymmetric walks.Comment: 11 pages, 11 figure
Non-stationary quantum walks on the cycle
We consider quantum walks on the cycle in the non-stationary case where the
`coin' operation is allowed to change at each time step. We characterize, in
algebraic terms, the set of possible state transfers and prove that, as opposed
to the stationary case, it is possible to asymnptotically reach a uniform
distribution among the nodes of the associated graph.Comment: Revised version with minor change
Quantum phase transition using quantum walks in an optical lattice
We present an approach using quantum walks (QWs) to redistribute ultracold
atoms in an optical lattice. Different density profiles of atoms can be
obtained by exploiting the controllable properties of QWs, such as the variance
and the probability distribution in position space using quantum coin
parameters and engineered noise. The QW evolves the density profile of atoms in
a superposition of position space resulting in a quadratic speedup of the
process of quantum phase transition. We also discuss implementation in
presently available setups of ultracold atoms in optical lattices.Comment: 7 pages, 8 figure
Quantum simulation of bosonic-fermionic non-interacting particles in disordered systems via quantum walk
We report on the theoretical analysis of bosonic and fermionic
non-interacting systems in a discrete two-particle quantum walk affected by
different kinds of disorder. We considered up to 100-step QWs with a spatial,
temporal and space-temporal disorder observing how the randomness and the
wavefunction symmetry non-trivially affect the final spatial probability
distribution, the transport properties and the Shannon entropy of the walkers.Comment: 13 pages, 10 figures. arXiv admin note: text overlap with
arXiv:1101.2638 by other author
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