28,731 research outputs found
Quantum Computational Complexity in the Presence of Closed Timelike Curves
Quantum computation with quantum data that can traverse closed timelike
curves represents a new physical model of computation. We argue that a model of
quantum computation in the presence of closed timelike curves can be formulated
which represents a valid quantification of resources given the ability to
construct compact regions of closed timelike curves. The notion of
self-consistent evolution for quantum computers whose components follow closed
timelike curves, as pointed out by Deutsch [Phys. Rev. D {\bf 44}, 3197
(1991)], implies that the evolution of the chronology respecting components
which interact with the closed timelike curve components is nonlinear. We
demonstrate that this nonlinearity can be used to efficiently solve
computational problems which are generally thought to be intractable. In
particular we demonstrate that a quantum computer which has access to closed
timelike curve qubits can solve NP-complete problems with only a polynomial
number of quantum gates.Comment: 8 pages, 2 figures. Minor changes and typos fixed. Reference adde
Dressing the chopped-random-basis optimization: a bandwidth-limited access to the trap-free landscape
In quantum optimal control theory the success of an optimization algorithm is
highly influenced by how the figure of merit to be optimized behaves as a
function of the control field, i.e. by the control landscape. Constraints on
the control field introduce local minima in the landscape --false traps-- which
might prevent an efficient solution of the optimal control problem. Rabitz et
al. [Science 303, 1998 (2004)] showed that local minima occur only rarely for
unconstrained optimization. Here, we extend this result to the case of
bandwidth-limited control pulses showing that in this case one can eliminate
the false traps arising from the constraint. Based on this theoretical
understanding, we modify the Chopped Random Basis (CRAB) optimal control
algorithm and show that this development exploits the advantages of both
(unconstrained) gradient algorithms and of truncated basis methods, allowing to
always follow the gradient of the unconstrained landscape by bandwidth-limited
control functions. We study the effects of additional constraints and show that
for reasonable constraints the convergence properties are still maintained.
Finally, we numerically show that this approach saturates the theoretical bound
on the minimal bandwidth of the control needed to optimally drive the system.Comment: 8 pages, 6 figure
Classical Topological Order in Kagome Ice
We examine the onset of classical topological order in a nearest-neighbor
kagome ice model. Using Monte Carlo simulations, we characterize the
topological sectors of the groundstate using a non-local cut measure which
circumscribes the toroidal geometry of the simulation cell. We demonstrate that
simulations which employ global loop updates that are allowed to wind around
the periodic boundaries cause the topological sector to fluctuate, while
restricted local loop updates freeze the simulation into one topological
sector. The freezing into one topological sector can also be observed in the
susceptibility of the real magnetic spin vectors projected onto the kagome
plane. The ability of the susceptibility to distinguish between fluctuating and
non-fluctuating topological sectors should motivate its use as a local probe of
topological order in a variety of related model and experimental systems.Comment: 17 pages, 9 figure
Fast Image Recovery Using Variable Splitting and Constrained Optimization
We propose a new fast algorithm for solving one of the standard formulations
of image restoration and reconstruction which consists of an unconstrained
optimization problem where the objective includes an data-fidelity
term and a non-smooth regularizer. This formulation allows both wavelet-based
(with orthogonal or frame-based representations) regularization or
total-variation regularization. Our approach is based on a variable splitting
to obtain an equivalent constrained optimization formulation, which is then
addressed with an augmented Lagrangian method. The proposed algorithm is an
instance of the so-called "alternating direction method of multipliers", for
which convergence has been proved. Experiments on a set of image restoration
and reconstruction benchmark problems show that the proposed algorithm is
faster than the current state of the art methods.Comment: Submitted; 11 pages, 7 figures, 6 table
General Relativistic Three-Dimensional Multi-Group Neutrino Radiation-Hydrodynamics Simulations of Core-Collapse Supernovae
We report on a set of long-term general-relativistic three-dimensional (3D)
multi-group (energy-dependent) neutrino-radiation hydrodynamics simulations of
core-collapse supernovae. We employ a full 3D two-moment scheme with the local
M1 closure, three neutrino species, and 12 energy groups per species. With
this, we follow the post-core-bounce evolution of the core of a nonrotating
- progenitor in full unconstrained 3D and in octant symmetry for
. We find the development of an asymmetric runaway
explosion in our unconstrained simulation. We test the resolution dependence of
our results and, in agreement with previous work, find that low resolution
artificially aids explosion and leads to an earlier runaway expansion of the
shock. At low resolution, the octant and full 3D dynamics are qualitatively
very similar, but at high resolution, only the full 3D simulation exhibits the
onset of explosion.Comment: Accepted to Ap
Cosmological Luminosity Evolution of QSO/AGN Population
We apply the observed optical/X-ray spectral states of the Galactic black
hole candidates (GBHCs) to the cosmological QSO luminosity evolution under the
assumptions that QSOs and GBHCs are powered by similar accretion processes and
that their emission mechanisms are also similar. The QSO luminosity function
(LF) evolution in various energy bands is strongly affected by the spectral
evolution which is tightly correlated with the luminosity evolution. We
generate a random sample of QSOs born nearly synchronously by allowing the QSOs
to have redshifts in a narrow range around an initial high redshift, black hole
masses according to a power-law, and mass accretion rates near Eddington rates.
The QSOs evolve as a single long-lived population on the cosmological time
scale. The pure luminosity evolution results in distinct luminosity evolution
features due to the strong spectral evolution. Most notably, different energy
bands (optical/UV, soft X-ray, and hard X-ray) show different evolutionary
trends and the hard X-ray LF in particular shows an apparent reversal of the
luminosity evolution (from decreasing to increasing luminosity) at low
redshifts, which is not seen in the conventional pure luminosity evolution
scenario without spectral evolution. The resulting mass function of black holes
(BHs), which is qualitatively consistent with the observed QSO LF evolution,
shows that QSO remnants are likely to be found as BHs with masses in the range
10**8-5x10**10 solar masses. The long-lived single population of QSOs are
expected to leave their remnants as supermassive BHs residing in rare, giant
elliptical galaxies.Comment: 9 pages, 2 figures, ApJ
Plasticity size effects in tension and compression of single crystals
The effect of size and loading conditions on the tension and compression stress–strain response of micron-sized planar crystals is investigated using discrete dislocation plasticity. The crystals are taken to have a single active slip system and both small-strain and finite-strain analyses are carried out. When rotation of the tensile axis is constrained, the build-up of geometrically necessary dislocations results in a weak size dependence but a strong Bauschinger effect. On the other hand, when rotation of the tensile axis is unconstrained, there is a strong size dependence, with the flow strength increasing with decreasing specimen size, and a negligible Bauschinger effect. Below a certain specimen size, the flow strength of the crystals is set by the nucleation strength of the initially present Frank–Read sources. The main features of the size dependence are the same for the small-strain and finite-strain analyses. However, the predicted hardening rates differ and the finite-strain analyses give rise to some tension–compression asymmetry.
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