10,434 research outputs found
Quantum Adversarial Learning in Emulation of Monte-Carlo Methods for Max-cut Approximation: QAOA is not optimal
One of the leading candidates for near-term quantum advantage is the class of
Variational Quantum Algorithms, but these algorithms suffer from classical
difficulty in optimizing the variational parameters as the number of parameters
increases. Therefore, it is important to understand the expressibility and
power of various ans\"atze to produce target states and distributions. To this
end, we apply notions of emulation to Variational Quantum Annealing and the
Quantum Approximate Optimization Algorithm (QAOA) to show that QAOA is
outperformed by variational annealing schedules with equivalent numbers of
parameters. Our Variational Quantum Annealing schedule is based on a novel
polynomial parameterization that can be optimized in a similar gradient-free
way as QAOA, using the same physical ingredients. In order to compare the
performance of ans\"atze types, we have developed statistical notions of
Monte-Carlo methods. Monte-Carlo methods are computer programs that generate
random variables that approximate a target number that is computationally hard
to calculate exactly. While the most well-known Monte-Carlo method is
Monte-Carlo integration (e.g. Diffusion Monte-Carlo or path-integral quantum
Monte-Carlo), QAOA is itself a Monte-Carlo method that finds good solutions to
NP-complete problems such as Max-cut. We apply these statistical Monte-Carlo
notions to further elucidate the theoretical framework around these quantum
algorithms
Cosmic Censorship: As Strong As Ever
Spacetimes which have been considered counter-examples to strong cosmic
censorship are revisited. We demonstrate the classical instability of the
Cauchy horizon inside charged black holes embedded in de Sitter spacetime for
all values of the physical parameters. The relevant modes which maintain the
instability, in the regime which was previously considered stable, originate as
outgoing modes near to the black hole event horizon. This same mechanism is
also relevant for the instability of Cauchy horizons in other proposed
counter-examples of strong cosmic censorship.Comment: 4 pages RevTeX style, 1 figure included using epsfi
Homothetic Wyman Spacetimes
The time-dependent, spherically symmetric, Wyman sector of the Unified Field
Theory is shown to be equivalent to a self-gravitating scalar field with a
positive-definite, repulsive self-interaction potential. A homothetic symmetry
is imposed on the fundamental tensor, and the resulting autonomous system is
numerically integrated. Near the critical point (between the collapsing and
non-collapsing spacetimes) the system displays an approximately periodic
alternation between collapsing and dispersive epochs.Comment: 15 pages with 6 figures; requires amsart, amssymb, amsmath, graphicx;
formatted for publication in Int. J. Mod. Phys.
A nonlinear detection algorithm for periodic signals in gravitational wave detectors
We present an algorithm for the detection of periodic sources of
gravitational waves with interferometric detectors that is based on a special
symmetry of the problem: the contributions to the phase modulation of the
signal from the earth rotation are exactly equal and opposite at any two
instants of time separated by half a sidereal day; the corresponding is true
for the contributions from the earth orbital motion for half a sidereal year,
assuming a circular orbit. The addition of phases through multiplications of
the shifted time series gives a demodulated signal; specific attention is given
to the reduction of noise mixing resulting from these multiplications. We
discuss the statistics of this algorithm for all-sky searches (which include a
parameterization of the source spin-down), in particular its optimal
sensitivity as a function of required computational power. Two specific
examples of all-sky searches (broad-band and narrow-band) are explored
numerically, and their performances are compared with the stack-slide technique
(P. R. Brady, T. Creighton, Phys. Rev. D, 61, 082001).Comment: 9 pages, 3 figures, to appear in Phys. Rev.
Speech Communication
Contains reports on four research projects.U. S. Air Force (Air Force Cambridge Research Center, Air Research and Development Command) under Contract AF19(604)-6102National Science Foundatio
Spacetime structure of static solutions in Gauss-Bonnet gravity: charged case
We have studied spacetime structures of static solutions in the
-dimensional Einstein-Gauss-Bonnet-Maxwell- system. Especially we
focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet
coefficient is non-negative and in
order to define the relevant vacuum state. Solutions have the
-dimensional Euclidean sub-manifold whose curvature is , or -1.
In Gauss-Bonnet gravity, solutions are classified into plus and minus branches.
In the plus branch all solutions have the same asymptotic structure as those in
general relativity with a negative cosmological constant. The charge affects a
central region of the spacetime. A branch singularity appears at the finite
radius for any mass parameter. There the Kretschmann invariant
behaves as , which is much milder than divergent behavior of
the central singularity in general relativity . Some charged
black hole solutions have no inner horizon in Gauss-Bonnet gravity. Although
there is a maximum mass for black hole solutions in the plus branch for
in the neutral case, no such maximum exists in the charged case. The solutions
in the plus branch with and have an "inner" black hole, and
inner and the "outer" black hole horizons. Considering the evolution of black
holes, we briefly discuss a classical discontinuous transition from one black
hole spacetime to another.Comment: 20 pages, 10 figure
Existence of naked singularities in Brans-Dicke theory of gravitation. An analytical and numerical study
Within the framework of the scalar-tensor models of gravitation and by
relying on analytical and numerical techniques, we establish the existence of a
class of spherically symmetric spacetimes containing a naked singularity. Our
result relies on and extends a work by Christodoulou on the existence of naked
singularities for the Einstein-scalar field equations. We establish that a key
parameter in Christodoulou's construction couples to the Brans-Dicke field and
becomes a dynamical variable, which enlarges and modifies the phase space of
solutions. We recover analytically many properties first identified by
Christodoulou, in particular the loss of regularity (especially at the center),
and then investigate numerically the properties of these spacetimes.Comment: 26 pages, PACS numbers: 04.20.Dw, 04.25.dc, 04.50.K
Gravitational collapse from smooth initial data with vanishing radial pressure
We study here the spherical gravitational collapse assuming initial data to
be necessarily smooth, as motivated by the requirements based on physical
reasonableness. A tangential pressure model is constructed and analyzed in
order to understand the final fate of collapse explicitly in terms of the
density and pressure parameters at the initial epoch from which the
collapsedevelops. It is seen that both black holes and naked singularities are
produced as collapse end states even when the initial data is smooth. We show
that the outcome is decided entirely in terms of the initial data, as given by
density, pressure and velocity profiles at the initial epoch, from which the
collapse evolves.Comment: 10 pages,3 figures,revtex4,Revised Versio
The effect of fabric strain during pressure steaming on fabric dimensional properties
It is shown that tension applied to fabric which is then permanently set by steaming under pressure for a short time has a significant effect on fabric dimensional properties. Increasing levels of stretch applied to fabric before pressure steaming resulted in decreases in fabric hygral expansion and relaxation shrinkage and also lowered fabric shrinkage that resulted from permanent setting. The setting conditions resembled those used in conventional pressure decatising, and it is suggested that in batch decatising, precise control of the length and width of fabric as it is batched up with the wrapper before steaming under pressure could enable predictable changes in fabric dimensions, relaxation shrinkage and hygral expansion to be obtained. <br /
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