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"Grids (Cartography)"
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Quantum error correction of a qubit encoded in grid states of an oscillator
The accuracy of logical operations on quantum bits (qubits) must be improved for quantum computers to outperform classical ones in useful tasks. One method to achieve this is quantum error correction (QEC), which prevents noise in the underlying system from causing logical errors. This approach derives from the reasonable assumption that noise is local, that is, it does not act in a coordinated way on different parts of the physical system. Therefore, if a logical qubit is encoded non-locally, we can—for a limited time—detect and correct noise-induced evolution before it corrupts the encoded information
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. In 2001, Gottesman, Kitaev and Preskill (GKP) proposed a hardware-efficient instance of such a non-local qubit: a superposition of position eigenstates that forms grid states of a single oscillator
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. However, the implementation of measurements that reveal this noise-induced evolution of the oscillator while preserving the encoded information
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–
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has proved to be experimentally challenging, and the only realization reported so far relied on post-selection
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,
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, which is incompatible with QEC. Here we experimentally prepare square and hexagonal GKP code states through a feedback protocol that incorporates non-destructive measurements that are implemented with a superconducting microwave cavity having the role of the oscillator. We demonstrate QEC of an encoded qubit with suppression of all logical errors, in quantitative agreement with a theoretical estimate based on the measured imperfections of the experiment. Our protocol is applicable to other continuous-variable systems and, in contrast to previous implementations of QEC
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–
14
, can mitigate all logical errors generated by a wide variety of noise processes and facilitate fault-tolerant quantum computation.
Quantum error correction of Gottesman–Kitaev–Preskill code states is realized experimentally in a superconducting quantum device.
Journal Article
Membrane potential dynamics of grid cells
During navigation, grid cells increase their spike rates in firing fields arranged on a markedly regular triangular lattice, whereas their spike timing is often modulated by theta oscillations. Oscillatory interference models of grid cells predict theta amplitude modulations of membrane potential during firing field traversals, whereas competing attractor network models predict slow depolarizing ramps. Here, using in vivo whole-cell recordings, we tested these models by directly measuring grid cell intracellular potentials in mice running along linear tracks in virtual reality. Grid cells had large and reproducible ramps of membrane potential depolarization that were the characteristic signature tightly correlated with firing fields. Grid cells also demonstrated intracellular theta oscillations that influenced their spike timing. However, the properties of theta amplitude modulations were not consistent with the view that they determine firing field locations. Our results support cellular and network mechanisms in which grid fields are produced by slow ramps, as in attractor models, whereas theta oscillations control spike timing.
Journal Article
Liberty's grid : a founding father, a mathematical dreamland, and the shaping of America
The surprising history behind a ubiquitous facet of America - the gridded landscape. From the halls of Congress to the open prairies, and from the fight against George III to the Trail of Tears, 'Liberty's Grid' tells the story of the battle between grid makers and their opponents. When Congress endorsed Jefferson's plan, it set off a struggle over American space that has not subsided. Transcendentalists, urban reformers, and conservationists saw the grid not as a place of possibility but as an artificial imposition that crushed the human spirit. Today, the ideas Jefferson associated with the grid still echo through political rhetoric about the country's founding, and competing visions for the nation are visible from Manhattan avenues and Kansan pastures to Yosemite's cliffs and suburbia's cul-de-sacs. An engrossing read, this book offers a powerful look at the ideological conflict written on the landscape.
BOOK
Gridded population mapping for Germany based on building density, height and type from Earth Observation data using census disaggregation and bottom-up estimates
Gridded population data is widely used to map fine scale population patterns and dynamics to understand associated human-environmental processes for global change research, disaster risk assessment and other domains. This study mapped gridded population across Germany using weighting layers from building density, building height (both from previous studies) and building type datasets, all created from freely available, temporally and globally consistent Copernicus Sentinel-1 and Sentinel-2 data. We first produced and validated a nation-wide dataset of predominant residential and non-residential building types. We then examined the impact of different weighting layers from density, type and height on top-down dasymetric mapping quality across scales. We finally performed a nation-wide bottom-up population estimate based on the three datasets. We found that integrating building types into dasymetric mapping is helpful at fine scale, as population is not redistributed to non-residential areas. Building density improved the overall quality of population estimates at all scales compared to using a binary building layer. Most importantly, we found that the combined use of density and height, i.e. volume, considerably increased mapping quality in general and with regard to regional discrepancy by largely eliminating systematic underestimation in dense agglomerations and overestimation in rural areas. We also found that building density, type and volume, together with living floor area per capita, are suitable to produce accurate large-area bottom-up population estimates.
Journal Article
A Multi-Resolution Approach to Point Cloud Registration without Control Points
Terrestrial photographic imagery combined with structure-from-motion (SfM) provides a relatively easy-to-implement method for monitoring environmental systems, even in remote and rough terrain. However, the collection of in-situ positioning data and the identification of control points required for georeferencing in SfM processing is the primary roadblock to using SfM in difficult-to-access locations; it is also the primary bottleneck for using SfM in a time series. We describe a novel, computationally efficient, and semi-automated approach for georeferencing unreferenced point clouds (UPC) derived from terrestrial overlapping photos to a reference dataset (e.g., DEM or aerial point cloud; hereafter RPC) in order to address this problem. The approach utilizes a Discrete Global Grid System (DGGS), which allows us to capitalize on easily collected rough information about camera deployment to coarsely register the UPC using the RPC. The DGGS also provides a hierarchical set of grids which supports a hierarchical modified iterative closest point algorithm with natural correspondence between the UPC and RPC. The approach requires minimal interaction in a user-friendly interface, while allowing for user adjustment of parameters and inspection of results. We illustrate the approach with two case studies: a close-range (<1 km) vertical glacier calving front reconstructed from two cameras at Fountain Glacier, Nunavut and a long-range (>3 km) scene of relatively flat glacier ice reconstructed from four cameras overlooking Nàłùdäy (Lowell Glacier), Yukon, Canada. We assessed the accuracy of the georeferencing by comparing the UPC to the RPC, as well as surveyed control points; the consistency of the registration was assessed using the difference between successive registered surfaces in the time series. The accuracy of the registration is roughly equal to the ground sampling distance and is consistent across time steps. These results demonstrate the promise of the approach for easy-to-implement georeferencing of point clouds from terrestrial imagery with acceptable accuracy, opening the door for new possibilities in remote monitoring for change-detection, such as monitoring calving rates, glacier surges, or other seasonal changes at remote field locations.
Journal Article
A GPU-Based Integration Method from Raster Data to a Hexagonal Discrete Global Grid
This paper proposes an algorithm for the conversion of raster data to hexagonal DGGSs in the GPU by redevising the encoding and decoding mechanisms. The researchers first designed a data structure based on rhombic tiles to convert the hexagonal DGGS to a texture format acceptable for GPUs, thus avoiding the irregularity of the hexagonal DGGS. Then, the encoding and decoding methods of the tile data based on space-filling curves were designed, respectively, so as to reduce the amount of data transmission from the CPU to the GPU. Finally, the researchers improved the algorithmic efficiency through thread design. To validate the above design, raster integration experiments were conducted based on the global Aster 30 m digital elevation dataDEM, and the experimental results showed that the raster integration accuracy of this algorithms was around 1 m, while its efficiency could be improved to more than 600 times that of the algorithm for integrating the raster data to the hexagonal DGGS data, executed in the CPU. Therefore, the researchers believe that this study will provide a feasible method for the efficient and stable integration of massive raster data based on a hexagonal grid, which may well support the organization of massive raster data in the field of GIS.
Journal Article
First order explicit time integration scheme with large time steps for parabolic problems using irregular grids
The authors thank Rainald Löhner for many useful discussions. The authors acknowledge the support from the MCIN/AEI of the Government of Spain and the FEDER programme of the EU for funding this work through project PID2021_122676NB-100.
Journal Article