27,733 research outputs found
On the Complexity of Random Quantum Computations and the Jones Polynomial
There is a natural relationship between Jones polynomials and quantum
computation. We use this relationship to show that the complexity of evaluating
relative-error approximations of Jones polynomials can be used to bound the
classical complexity of approximately simulating random quantum computations.
We prove that random quantum computations cannot be classically simulated up to
a constant total variation distance, under the assumption that (1) the
Polynomial Hierarchy does not collapse and (2) the average-case complexity of
relative-error approximations of the Jones polynomial matches the worst-case
complexity over a constant fraction of random links. Our results provide a
straightforward relationship between the approximation of Jones polynomials and
the complexity of random quantum computations.Comment: 8 pages, 4 figure
HILTOP supplement: Heliocentric interplanetary low thrust trajectory optimization program, supplement 1
Modifications and improvements are described that were made to the HILTOP electric propulsion trajectory optimization computer program during calendar years 1973 and 1974. New program features include the simulation of power degradation, housekeeping power, launch asymptote declination optimization, and powered and unpowered ballistic multiple swingby missions with an optional deep space burn
3-Body Dynamics in a (1+1) Dimensional Relativistic Self-Gravitating System
The results of our study of the motion of a three particle, self-gravitating
system in general relativistic lineal gravity is presented for an arbitrary
ratio of the particle masses. We derive a canonical expression for the
Hamiltonian of the system and discuss the numerical solution of the resulting
equations of motion. This solution is compared to the corresponding
non-relativistic and post-Newtonian approximation solutions so that the
dynamics of the fully relativistic system can be interpretted as a correction
to the one-dimensional Newtonian self-gravitating system. We find that the
structure of the phase space of each of these systems yields a large variety of
interesting dynamics that can be divided into three distinct regions: annulus,
pretzel, and chaotic; the first two being regions of quasi-periodicity while
the latter is a region of chaos. By changing the relative masses of the three
particles we find that the relative sizes of these three phase space regions
changes and that this deformation can be interpreted physically in terms of the
gravitational interactions of the particles. Furthermore, we find that many of
the interesting characteristics found in the case where all of the particles
share the same mass also appears in our more general study. We find that there
are additional regions of chaos in the unequal mass system which are not
present in the equal mass case. We compare these results to those found in
similar systems.Comment: latex, 26 pages, 17 figures, high quality figures available upon
request; typos and grammar correcte
Heliocentric interplanetary low thrust trajectory optimization program, supplement 1, part 2
The improvements made to the HILTOP electric propulsion trajectory computer program are described. A more realistic propulsion system model was implemented in which various thrust subsystem efficiencies and specific impulse are modeled as variable functions of power available to the propulsion system. The number of operating thrusters are staged, and the beam voltage is selected from a set of five (or less) constant voltages, based upon the application of variational calculus. The constant beam voltages may be optimized individually or collectively. The propulsion system logic is activated by a single program input key in such a manner as to preserve the HILTOP logic. An analysis describing these features, a complete description of program input quantities, and sample cases of computer output illustrating the program capabilities are presented
Selected solar electric propulsion and ballistic missions studies
Selected missions using solar electric propulsion and conventional propulsion systems were studied. The accomplishment of the tasks required extensive modification of the trajectory optimization computer program HILTOP. In addition to adding new program features, HILTOP was completely restructured to reduce execution time. The specific mission studies reported on are the direct and Venus swingby missions to the comet Encke and solar electric propulsion missions to Encke and to a distance of 0.25 AU from the sun
Heliocentric interplanetary low thrust trajectory optimization program, supplement 1
The modifications and improvements made to the HILTOP electric propulsion trajectory optimization computer program up through the end of 1974 is described. New program features include the simulation of power degradation, housekeeping power, launch asymptote declination optimization, and powered and unpowered ballistic multiple swingby missions with an optional deep space burn. The report contains the new analysis describing these features, a complete description of program input quantities, and sample cases of computer output illustrating the new program capabilities
Solar electric propulsion mission requirements study Final report
Analysis of solar electric propulsion for unmanned exploration of solar syste
Quasiclassical Coarse Graining and Thermodynamic Entropy
Our everyday descriptions of the universe are highly coarse-grained,
following only a tiny fraction of the variables necessary for a perfectly
fine-grained description. Coarse graining in classical physics is made natural
by our limited powers of observation and computation. But in the modern quantum
mechanics of closed systems, some measure of coarse graining is inescapable
because there are no non-trivial, probabilistic, fine-grained descriptions.
This essay explores the consequences of that fact. Quantum theory allows for
various coarse-grained descriptions some of which are mutually incompatible.
For most purposes, however, we are interested in the small subset of
``quasiclassical descriptions'' defined by ranges of values of averages over
small volumes of densities of conserved quantities such as energy and momentum
and approximately conserved quantities such as baryon number. The
near-conservation of these quasiclassical quantities results in approximate
decoherence, predictability, and local equilibrium, leading to closed sets of
equations of motion. In any description, information is sacrificed through the
coarse graining that yields decoherence and gives rise to probabilities for
histories. In quasiclassical descriptions, further information is sacrificed in
exhibiting the emergent regularities summarized by classical equations of
motion. An appropriate entropy measures the loss of information. For a
``quasiclassical realm'' this is connected with the usual thermodynamic entropy
as obtained from statistical mechanics. It was low for the initial state of our
universe and has been increasing since.Comment: 17 pages, 0 figures, revtex4, Dedicated to Rafael Sorkin on his 60th
birthday, minor correction
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