4,183 research outputs found
Continuous-time quantum walks on dynamical percolation graphs
We address continuous-time quantum walks on graphs in the presence of time-
and space-dependent noise. Noise is modeled as generalized dynamical
percolation, i.e. classical time-dependent fluctuations affecting the tunneling
amplitudes of the walker. In order to illustrate the general features of the
model, we review recent results on two paradigmatic examples: the dynamics of
quantum walks on the line and the effects of noise on the performances of
quantum spatial search on the complete and the star graph. We also discuss
future perspectives, including extension to many-particle quantum walk, to
noise model for on-site energies and to the analysis of different noise
spectra. Finally, we address the use of quantum walks as a quantum probe to
characterize defects and perturbations occurring in complex, classical and
quantum, networks.Comment: 7 pages, 4 figures. Accepted for publication in EPL Perspective
Effective description of the short-time dynamics in open quantum systems
We address the dynamics of a bosonic system coupled to either a bosonic or a
magnetic environment, and derive a set of sufficient conditions that allow one
to describe the dynamics in terms of the effective interaction with a classical
fluctuating field. We find that for short interaction times the dynamics of the
open system is described by a Gaussian noise map for several different
interaction models and independently on the temperature of the environment. In
order to go beyond a qualitative understanding of the origin and physical
meaning of the above short-time constraint, we take a general viewpoint and,
based on an algebraic approach, suggest that any quantum environment can be
described by classical fields whenever global symmetries lead to the definition
of environmental operators that remain well defined when increasing the size,
i.e. the number of dynamical variables, of the environment. In the case of the
bosonic environment this statement is exactly demonstrated via a constructive
procedure that explicitly shows why a large number of environmental dynamical
variables and, necessarily, global symmetries, entail the set of conditions
derived in the first part of the work.Comment: 9 pages, close to published versio
Non-Markovianity by undersampling in quantum optical simulators
We unveil a novel source of non-Markovianity for the dynamics of quantum
systems, which appears when the system does not explore the full set of
dynamical trajectories in the interaction with its environment. We term this
effect non-Markovianity by undersampling and demonstrate its appearance in the
operation of an all-optical quantum simulator involving a polarization qubit
interacting with a dephasing fluctuating environment.Comment: Accepted versio
Quantum spatial search on graphs subject to dynamical noise
We address quantum spatial search on graphs and its implementation by
continuous-time quantum walks in the presence of dynamical noise. In
particular, we focus on search on the complete graph and on the star graph of
order , proving that also the latter is optimal in the computational limit
, being nearly optimal also for small . The noise is modeled by
independent sources of random telegraph noise (RTN), dynamically perturbing the
links of the graph. We observe two different behaviours depending on the
switching rate of RTN: fast noise only slightly degrades performance, whereas
slow noise is more detrimental and, in general, lowers the success probability.
In particular, we still find a quadratic speed-up for the average running time
of the algorithm, while for the star graph with external target node we observe
a transition to classical scaling. We also address how the effects of noise
depend on the order of the graphs, and discuss the role of the graph topology.
Overall, our results suggest that realizations of quantum spatial search are
possible with current technology, and also indicate the star graph as the
perfect candidate for the implementation by noisy quantum walks, owing to its
simple topology and nearly optimal performance also for just few nodes.Comment: Accepted versio
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