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-$d$ 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 $SU(d)$ for $d=2$ 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