16 research outputs found
Noise enhanced performance of adiabatic quantum computing by lifting degeneracies
We investigate the symmetry breaking role of noise in adiabatic quantum
computing using the example of the CNOT gate. In particular, we analyse
situations where the choice of initial configuration leads to symmetries in the
Hamiltonian and degeneracies in the spectrum. We show that, in these
situations, there exists an optimal level of noise that maximises the success
probability and the fidelity of the final state. The effects of an artificial
noise source with a time-dependent amplitude are also explored and it is found
that such a scheme would offer a considerable performance enhancement.Comment: 12 pages and 4 figures in preprint format. References in article
corrected and journal reference adde
The Poincare-Birkhoff theorem in Quantum Mechanics
Quantum manifestations of the dynamics around resonant tori in perturbed
Hamiltonian systems, dictated by the Poincar\'e--Birkhoff theorem, are shown to
exist. They are embedded in the interactions involving states which differ in a
number of quanta equal to the order of the classical resonance. Moreover, the
associated classical phase space structures are mimicked in the
quasiprobability density functions and their zeros.Comment: 5 pages, 3 figures, Full resolution figures available at
http://www.df.uba.ar/users/wisniaki/publications.htm
Extremal spacings between eigenphases of random unitary matrices and their tensor products
Extremal spacings between eigenvalues of random unitary matrices of size N
pertaining to circular ensembles are investigated. Explicit probability
distributions for the minimal spacing for various ensembles are derived for N =
4. We study ensembles of tensor product of k random unitary matrices of size n
which describe independent evolution of a composite quantum system consisting
of k subsystems. In the asymptotic case, as the total dimension N = n^k becomes
large, the nearest neighbor distribution P(s) becomes Poissonian, but
statistics of extreme spacings P(s_min) and P(s_max) reveal certain deviations
from the Poissonian behavior
Integrability and action operators in quantum Hamiltonian systems
For a (classically) integrable quantum mechanical system with two degrees of
freedom, the functional dependence of the
Hamiltonian operator on the action operators is analyzed and compared with the
corresponding functional relationship in
the classical limit of that system. The former is shown to converge toward the
latter in some asymptotic regime associated with the classical limit, but the
convergence is, in general, non-uniform. The existence of the function
in the integrable regime of a parametric
quantum system explains empirical results for the dimensionality of manifolds
in parameter space on which at least two levels are degenerate. The comparative
analysis is carried out for an integrable one-parameter two-spin model.
Additional results presented for the (integrable) circular billiard model
illuminate the same conclusions from a different angle.Comment: 9 page
Computationally efficient method to construct scar functions
Phys. Rev. E 85, 026214-026219 (2012) Desarrollo de un nuevo y eficiente método para la construcción de funciones de scar a lo largo de las órtbitas periódicas inestables de sistemas clásicamente caótico
Entanglement production in Quantized Chaotic Systems
Quantum chaos is a subject whose major goal is to identify and to investigate
different quantum signatures of classical chaos. Here we study entanglement
production in coupled chaotic systems as a possible quantum indicator of
classical chaos. We use coupled kicked tops as a model for our extensive
numerical studies. We find that, in general, presence of chaos in the system
produces more entanglement. However, coupling strength between two subsystems
is also very important parameter for the entanglement production. Here we show
how chaos can lead to large entanglement which is universal and describable by
random matrix theory (RMT). We also explain entanglement production in coupled
strongly chaotic systems by deriving a formula based on RMT. This formula is
valid for arbitrary coupling strengths, as well as for sufficiently long time.
Here we investigate also the effect of chaos on the entanglement production for
the mixed initial state. We find that many properties of the mixed state
entanglement production are qualitatively similar to the pure state
entanglement production. We however still lack an analytical understanding of
the mixed state entanglement production in chaotic systems.Comment: 16 pages, 5 figures. To appear in Pramana:Journal of Physic
Modeling Complex Nuclear Spectra - Regularity versus Chaos
A statistical analysis of the spectrum of two particle - two hole doorway
states in a finite nucleus is performed. On the unperturbed mean-field level
sizable attractive correlations are present in such a spectrum. Including
particle-hole rescattering effects via the residual interaction introduces
repulsive dynamical correlations which generate the fluctuation properties
characteristic of the Gaussian Orthogonal Ensemble. This signals that the
underlying dynamics becomes chaotic. This feature turns out to be independent
of the detailed form of the residual interaction and hence reflects the generic
nature of the fluctuations studied.Comment: 8 pages of text (LATEX), figures (not included, available from the
authors), Feb 9