683 research outputs found
The world problem: on the computability of the topology of 4-manifolds
Topological classification of the 4-manifolds bridges computation theory and
physics. A proof of the undecidability of the homeomorphy problem for
4-manifolds is outlined here in a clarifying way. It is shown that an arbitrary
Turing machine with an arbitrary input can be encoded into the topology of a
4-manifold, such that the 4-manifold is homeomorphic to a certain other
4-manifold if and only if the corresponding Turing machine halts on the
associated input. Physical implications are briefly discussed.Comment: Submitted to Class. Quant. Gra
Excising das All: Evolving Maxwell waves beyond scri
We study the numerical propagation of waves through future null infinity in a
conformally compactified spacetime. We introduce an artificial cosmological
constant, which allows us some control over the causal structure near null
infinity. We exploit this freedom to ensure that all light cones are tilted
outward in a region near null infinity, which allows us to impose
excision-style boundary conditions in our finite difference code. In this
preliminary study we consider electromagnetic waves propagating in a static,
conformally compactified spacetime.Comment: 13 pages; incorporated material from gr-qc/051216
Hydrogen safety Progress report no. 6, 1 Apr. - 30 Jun. 1965
Hydrogen safety hazards, storage, and handling - Hydrogen plume studies to determine quantity-distance criteria and guidelines for optimum placement of hydrogen detector
Hydrogen safety Progress report no. 7 1 Jul. - 30 Sep. 1965
Performance characteristics of two console-type hydrogen gas detectors sampling by diffusion and convectio
A high bandwidth quantum repeater
We present a physical- and link-level design for the creation of entangled
pairs to be used in quantum repeater applications where one can control the
noise level of the initially distributed pairs. The system can tune
dynamically, trading initial fidelity for success probability, from high
fidelity pairs (F=0.98 or above) to moderate fidelity pairs. The same physical
resources that create the long-distance entanglement are used to implement the
local gates required for entanglement purification and swapping, creating a
homogeneous repeater architecture. Optimizing the noise properties of the
initially distributed pairs significantly improves the rate of generating
long-distance Bell pairs. Finally, we discuss the performance trade-off between
spatial and temporal resources.Comment: 5 page
On the Effect of Quantum Interaction Distance on Quantum Addition Circuits
We investigate the theoretical limits of the effect of the quantum
interaction distance on the speed of exact quantum addition circuits. For this
study, we exploit graph embedding for quantum circuit analysis. We study a
logical mapping of qubits and gates of any -depth quantum adder
circuit for two -qubit registers onto a practical architecture, which limits
interaction distance to the nearest neighbors only and supports only one- and
two-qubit logical gates. Unfortunately, on the chosen -dimensional practical
architecture, we prove that the depth lower bound of any exact quantum addition
circuits is no longer , but . This
result, the first application of graph embedding to quantum circuits and
devices, provides a new tool for compiler development, emphasizes the impact of
quantum computer architecture on performance, and acts as a cautionary note
when evaluating the time performance of quantum algorithms.Comment: accepted for ACM Journal on Emerging Technologies in Computing
System
Reducing reflections from mesh refinement interfaces in numerical relativity
Full interpretation of data from gravitational wave observations will require
accurate numerical simulations of source systems, particularly binary black
hole mergers. A leading approach to improving accuracy in numerical relativity
simulations of black hole systems is through fixed or adaptive mesh refinement
techniques. We describe a manifestation of numerical interface truncation error
which appears as slowly converging, artificial reflections from refinement
boundaries in a broad class of mesh refinement implementations, potentially
compromising the effectiveness of mesh refinement techniques for some numerical
relativity applications if left untreated. We elucidate this numerical effect
by presenting a model problem which exhibits the phenomenon, but which is
simple enough that its numerical error can be understood analytically. Our
analysis shows that the effect is caused by variations in finite differencing
error generated across low and high resolution regions, and that its slow
convergence is caused by the presence of dramatic speed differences among
propagation modes typical of 3+1 relativity. Lastly, we resolve the problem,
presenting a class of finite differencing stencil modifications, termed
mesh-adapted differencing (MAD), which eliminate this pathology in both our
model problem and in numerical relativity examples.Comment: 7 page
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