1,067 research outputs found
Discrete Wigner Function Derivation of the Aaronson-Gottesman Tableau Algorithm
The Gottesman-Knill theorem established that stabilizer states and operations
can be efficiently simulated classically. For qudits with dimension three and
greater, stabilizer states and Clifford operations have been found to
correspond to positive discrete Wigner functions and dynamics. We present a
discrete Wigner function-based simulation algorithm for odd- qudits that has
the same time and space complexity as the Aaronson-Gottesman algorithm. We show
that the efficiency of both algorithms is due to the harmonic evolution in the
symplectic structure of discrete phase space. The differences between the
Wigner function algorithm and Aaronson-Gottesman are likely due only to the
fact that the Weyl-Heisenberg group is not in for and that qubits
have state-independent contextuality. This may provide a guide for extending
the discrete Wigner function approach to qubits
Minimal area surfaces in AdS_{n+1} and Wilson loops
The AdS/CFT correspondence relates the expectation value of Wilson loops in
N=4 SYM to the area of minimal surfaces in AdS_5
In this paper we consider minimal area surfaces in generic Euclidean
AdS_{n+1} using the Pohlmeyer reduction in a similar way as we did previously
in Euclidean AdS_3. As in that case, the main obstacle is to find the correct
parameterization of the curve in terms of a conformal parameter. Once that is
done, the boundary conditions for the Pohlmeyer fields are obtained in terms of
conformal invariants of the curve. After solving the Pohlmeyer equations, the
area can be expressed as a boundary integral involving a generalization of the
conformal arc-length, curvature and torsion of the curve. Furthermore, one can
introduce the \lambda-deformation symmetry of the contours by a simple change
in the conformal invariants. This determines the \lambda-deformed contours in
terms of the solution of a boundary linear problem. In fact the condition that
all \lambda deformed contours are periodic can be used as an alternative to
solving the Pohlmeyer equations and is equivalent to imposing the vanishing of
an infinite set of conserved charges derived from integrability.Comment: 29 pages, LaTeX, 1 figur
Pneumatic Sampling in Extreme Terrain with the Axel Rover
Some of the most interesting regions of study in our solar system lie inside craters, canyons, and
cryovolcanoes, but current state-of-the-art rovers are incapable of accessing and traversing these
regions. Axel is a minimalistic rover designed for extreme terrains, and two Axels with a central mother
system form a four-wheeled rover to efficiently traverse flat ground. Upon approaching the edge of a
crater, Axel detaches from the mother system and travels down the cliff guided by the unwinding tether.
However, scientific study of extraplanetary terrains requires instrumentation inside the Axel rover. We
aim to develop a simple and reliable sample acquisition and caching system that could retrieve multiple
samples from various sites before returning them to the mother system where more sophisticated
instruments could perform further analysis. For simplicity and robustness, we propose a pneumatic
sampling system which uses compressed air, guided with a nozzle, to blow soil into a sample canister.
Numerous types of nozzles were designed, built, and tested. Different designs for nozzle deployment,
sample caching, and pressure containment were considered. Finally, a prototype of the entire sampling
system was built and evaluated for performance and feasibility
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