Cellular-automaton decoders with provable thresholds for topological codes

We propose a new cellular automaton (CA), the Sweep Rule, which generalizes Toom's rule to any locally Euclidean lattice. We use the Sweep Rule to design a local decoder for the toric code in $d\geq 3$ dimensions, the Sweep Decoder, and rigorously establish a lower bound on its performance. We also numerically estimate the Sweep Decoder threshold for the three-dimensional toric code on the cubic and body-centered cubic lattices for phenomenological phase-flip noise. Our results lead to new CA decoders with provable error-correction thresholds for other topological quantum codes including the color code.Comment: 4+8 pages, 5 figure

Efficient color code decoders in d≥2d\geq 2 dimensions from toric code decoders

We introduce an efficient decoder of the color code in $d\geq 2$ dimensions, the Restriction Decoder, which uses any $d$-dimensional toric code decoder combined with a local lifting procedure to find a recovery operation. We prove that the Restriction Decoder successfully corrects errors in the color code if and only if the corresponding toric code decoding succeeds. We also numerically estimate the Restriction Decoder threshold for the color code in two and three dimensions against the bit-filp and phase-flip noise with perfect syndrome extraction. We report that the 2D color code threshold $p_{\textrm{2D}} \approx 10.2\%$ on the square-octagon lattice is on a par with the toric code threshold on the square lattice.Comment: 28 pages, 8 figure

LSST: Comprehensive NEO Detection, Characterization, and Orbits

(Abridged) The Large Synoptic Survey Telescope (LSST) is currently by far the most ambitious proposed ground-based optical survey. Solar System mapping is one of the four key scientific design drivers, with emphasis on efficient Near-Earth Object (NEO) and Potentially Hazardous Asteroid (PHA) detection, orbit determination, and characterization. In a continuous observing campaign of pairs of 15 second exposures of its 3,200 megapixel camera, LSST will cover the entire available sky every three nights in two photometric bands to a depth of V=25 per visit (two exposures), with exquisitely accurate astrometry and photometry. Over the proposed survey lifetime of 10 years, each sky location would be visited about 1000 times. The baseline design satisfies strong constraints on the cadence of observations mandated by PHAs such as closely spaced pairs of observations to link different detections and short exposures to avoid trailing losses. Equally important, due to frequent repeat visits LSST will effectively provide its own follow-up to derive orbits for detected moving objects. Detailed modeling of LSST operations, incorporating real historical weather and seeing data from LSST site at Cerro Pachon, shows that LSST using its baseline design cadence could find 90% of the PHAs with diameters larger than 250 m, and 75% of those greater than 140 m within ten years. However, by optimizing sky coverage, the ongoing simulations suggest that the LSST system, with its first light in 2013, can reach the Congressional mandate of cataloging 90% of PHAs larger than 140m by 2020.Comment: 10 pages, color figures, presented at IAU Symposium 23