9,429 research outputs found
Limitations of Quantum Coset States for Graph Isomorphism
It has been known for some time that graph isomorphism reduces to the hidden
subgroup problem (HSP). What is more, most exponential speedups in quantum
computation are obtained by solving instances of the HSP. A common feature of
the resulting algorithms is the use of quantum coset states, which encode the
hidden subgroup. An open question has been how hard it is to use these states
to solve graph isomorphism. It was recently shown by Moore, Russell, and
Schulman that only an exponentially small amount of information is available
from one, or a pair of coset states. A potential source of power to exploit are
entangled quantum measurements that act jointly on many states at once. We show
that entangled quantum measurements on at least \Omega(n log n) coset states
are necessary to get useful information for the case of graph isomorphism,
matching an information theoretic upper bound. This may be viewed as a negative
result because highly entangled measurements seem hard to implement in general.
Our main theorem is very general and also rules out using joint measurements on
few coset states for some other groups, such as GL(n, F_{p^m}) and G^n where G
is finite and satisfies a suitable property.Comment: 25 page
Minisuperspace results for causal dynamical triangulations
Detailed applications of minisuperspace methods are presented and compared
with results obtained in recent years by means of causal dynamical
triangulations (CDTs), mainly in the form of effective actions. The analysis
sheds light on conceptual questions such as the treatment of time or the role
and scaling behavior of statistical and quantum fluctuations. In the case of
fluctuations, several analytical and numerical results show agreement between
the two approaches and offer possible explanations of effects that have been
seen in causal dynamical triangulations but whose origin remained unclear. The
new approach followed here suggests `CDT experiments' in the form of new
simulations or evaluations motivated by theoretical predictions, testing CDTs
as well as the minisuperspace approximation.Comment: 51 pages, 16 figure
Computer Simulation of Particle Suspensions
Particle suspensions are ubiquitous in our daily life, but are not well
understood due to their complexity. During the last twenty years, various
simulation methods have been developed in order to model these systems. Due to
varying properties of the solved particles and the solvents, one has to choose
the simulation method properly in order to use the available compute resources
most effectively with resolving the system as well as needed. Various
techniques for the simulation of particle suspensions have been implemented at
the Institute for Computational Physics allowing us to study the properties of
clay-like systems, where Brownian motion is important, more macroscopic
particles like glass spheres or fibers solved in liquids, or even the pneumatic
transport of powders in pipes. In this paper we will present the various
methods we applied and developed and discuss their individual advantages.Comment: 31 pages, 11 figures, to appear in Lecture Notes in Applied and
Computational Mechanics, Springer (2006
Evaluating the Roles of Rainout and Post-Condensation Processes in a Landfalling Atmospheric River with Stable Isotopes in Precipitation and Water Vapor
Atmospheric rivers (ARs), and frontal systems more broadly, tend to exhibit prominent “V” shapes in time series of stable isotopes in precipitation. Despite the magnitude and widespread nature of these “V” shapes, debate persists as to whether these shifts are driven by changes in the degree of rainout, which we determine using the Rayleigh distillation of stable isotopes, or by post-condensation processes such as below-cloud evaporation and equilibrium isotope exchange between hydrometeors and surrounding vapor. Here, we present paired precipitation and water vapor isotope time series records from the 5–7 March 2016, AR in Bodega Bay, CA. The stable isotope composition of surface vapor along with independent meteorological constraints such as temperature and relative humidity reveal that rainout and post-condensation processes dominate during different portions of the event. We find that Rayleigh distillation controls during peak AR conditions (with peak rainout of 55%) while post-condensation processes have their greatest effect during periods of decreased precipitation on the margins of the event. These results and analyses inform critical questions regarding the temporal evolution of AR events and the physical processes that control them at local scales
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