1,804 research outputs found
Local vs. translationally-invariant slowest operators in quantum Ising spin chains
In this paper we study one-dimensional quantum Ising spin chains in external
magnetic field close to an integrable point. We concentrate on the dynamics of
the slowest operator, that plays a key role at the final period of
thermalization. We introduce two independent definitions of the slowest
operator: local and translationally-invariant ones. We construct both operators
numerically using tensor networks and extensively compare their physical
properties. We find that the local operator has a significant overlap with
energy flux, it does not correspond to an integral of motion, and, as one goes
away from the integrable point, its revivals get suppressed and the rate of
delocalization changes from extremely slow to slower than diffusion. The
translationally-invariant operator corresponds to an integral of motion; as the
system becomes less integrable, at some point this operator changes its nature:
from no overlap with any magnetization and fast rate of delocalization, to
non-zero overlap with magnetizations and and slow
rate of delocalization
Quantum computing of delocalization in small-world networks
We study a quantum small-world network with disorder and show that the system
exhibits a delocalization transition. A quantum algorithm is built up which
simulates the evolution operator of the model in a polynomial number of gates
for exponential number of vertices in the network. The total computational gain
is shown to depend on the parameters of the network and a larger than quadratic
speed-up can be reached.
We also investigate the robustness of the algorithm in presence of
imperfections.Comment: 4 pages, 5 figures, research done at
http://www.quantware.ups-tlse.fr
Recent results of quantum ergodicity on graphs and further investigation
We outline some recent proofs of quantum ergodicity on large graphs and give
new applications in the context of irregular graphs. We also discuss some
remaining questions.Comment: To appear in "Annales de la facult\'e des Sciences de Toulouse
Quantum Google in a Complex Network
We investigate the behavior of the recently proposed quantum Google
algorithm, or quantum PageRank, in large complex networks. Applying the quantum
algorithm to a part of the real World Wide Web, we find that the algorithm is
able to univocally reveal the underlying scale-free topology of the network and
to clearly identify and order the most relevant nodes (hubs) of the graph
according to their importance in the network structure. Moreover, our results
show that the quantum PageRank algorithm generically leads to changes in the
hierarchy of nodes. In addition, as compared to its classical counterpart, the
quantum algorithm is capable to clearly highlight the structure of secondary
hubs of the network, and to partially resolve the degeneracy in importance of
the low lying part of the list of rankings, which represents a typical
shortcoming of the classical PageRank algorithm. Complementary to this study,
our analysis shows that the algorithm is able to clearly distinguish scale-free
networks from other widespread and important classes of complex networks, such
as Erd\H{o}s-R\'enyi networks and hierarchical graphs. We show that the ranking
capabilities of the quantum PageRank algorithm are related to an increased
stability with respect to a variation of the damping parameter that
appears in the Google algorithm, and to a more clearly pronounced power-law
behavior in the distribution of importance among the nodes, as compared to the
classical algorithm. Finally, we study to which extent the increased
sensitivity of the quantum algorithm persists under coordinated attacks of the
most important nodes in scale-free and Erd\H{o}s-R\'enyi random graphs
Nonequilibrium phases in hybrid arrays with flux qubits and NV centers
We propose a startling hybrid quantum architecture for simulating a
localization-delocalization transition. The concept is based on an array of
superconducting flux qubits which are coupled to a diamond crystal containing
nitrogen-vacancy (NV) centers. The underlying description is a
Jaynes-Cummings-lattice in the strong-coupling regime. However, in contrast to
well-studied coupled cavity arrays the interaction between lattice sites is
mediated here by the qubit rather than by the oscillator degrees of freedom.
Nevertheless, we point out that a transition between a localized and a
delocalized phase occurs in this system as well. We demonstrate the possibility
of monitoring this transition in a non-equilibrium scenario, including
decoherence effects. The proposed scheme allows the monitoring of
localization-delocalization transitions in Jaynes-Cummings-lattices by use of
currently available experimental technology. Contrary to cavity-coupled
lattices, our proposed recourse to stylized qubit networks facilitates (i) to
investigate localization-delocalization transitions in arbitrary dimensions and
(ii) to tune the inter-site coupling in-situ.Comment: Version to be published in Phys. Rev.
S-matrix network models for coherent waves in random media: construction and renormalization
Networks of random quantum scatterers (S-matrices) form paradigmatic models
for the propagation of coherent waves in random S-matrix network models cover
universal localization-delocalization properties and have some advantages over
more traditional Hamiltonian models. In particular, a straightforward
implementation of real space renormalization techniques is possible. Starting
from a finite elementary cell of the S-matrix network, hierarchical network
models can be constructed by recursion. The localization-delocalization
properties are contained in the flow of the forward scattering strength
('conductance') under increasing system size. With the aid of 'small scale'
numerics qualitative aspects of the localization-delocalization properties of
S-matrix network models can be worked out.Comment: 10 pages, LaTeX, 8 eps figures included, proceedings PILS98, to be
published in Annalen der Physi
Topological delocalization in the completely disordered two-dimensional quantum walk
We investigate numerically and theoretically the effect of spatial disorder
on two-dimensional split-step discrete-time quantum walks with two internal
"coin" states. Spatial disorder can lead to Anderson localization, inhibiting
the spread of quantum walks, putting them at a disadvantage against their
diffusively spreading classical counterparts. We find that spatial disorder of
the most general type, i.e., position-dependent Haar random coin operators,
does not lead to Anderson localization but to a diffusive spread instead. This
is a delocalization, which happens because disorder places the quantum walk to
a critical point between different anomalous Floquet-Anderson insulating
topological phases. We base this explanation on the relationship of this
general quantum walk to a simpler case more studied in the literature and for
which disorder-induced delocalization of a topological origin has been
observed. We review topological delocalization for the simpler quantum walk,
using time evolution of the wave functions and level spacing statistics. We
apply scattering theory to two-dimensional quantum walks and thus calculate the
topological invariants of disordered quantum walks, substantiating the
topological interpretation of the delocalization and finding signatures of the
delocalization in the finite-size scaling of transmission. We show criticality
of the Haar random quantum walk by calculating the critical exponent in
three different ways and find 0.52 as in the integer quantum
Hall effect. Our results showcase how theoretical ideas and numerical tools
from solid-state physics can help us understand spatially random quantum walks.Comment: 18 pages, 18 figures. Similar to the published version. Comments are
welcom
- …