Automated detection of symmetry-protected subspaces in quantum simulations

The analysis of symmetry in quantum systems is of utmost theoretical importance, useful in a variety of applications and experimental settings, and is difficult to accomplish in general. Symmetries imply conservation laws, which partition Hilbert space into invariant subspaces of the time-evolution operator, each of which is demarcated according to its conserved quantity. We show that, starting from a chosen basis, any invariant, symmetry-protected subspaces which are diagonal in that basis are discoverable using transitive closure on graphs representing state-to-state transitions under $k$-local unitary operations. Importantly, the discovery of these subspaces relies neither upon the explicit identification of a symmetry operator or its eigenvalues nor upon the construction of matrices of the full Hilbert space dimension. We introduce two classical algorithms, which efficiently compute and elucidate features of these subspaces. The first algorithm explores the entire symmetry-protected subspace of an initial state in time complexity linear to the size of the subspace by closing local basis state-to-basis state transitions. The second algorithm determines, with bounded error, if a given measurement outcome of a dynamically-generated state is within the symmetry-protected subspace of the state in which the dynamical system is initialized. We demonstrate the applicability of these algorithms by performing post-selection on data generated from emulated noisy quantum simulations of three different dynamical systems: the Heisenberg-XXX model and the $T_6$ and $F_4$ quantum cellular automata. Due to their efficient computability and indifference to identifying the underlying symmetry, these algorithms lend themselves to the post-selection of quantum computer data, optimized classical simulation of quantum systems, and the discovery of previously hidden symmetries in quantum mechanical systems.Comment: 23 pages, 7 figures, 4 appendice

La Ley de Gresham, la inflación, la teoría subjetiva del valor, el control de precios y la usura en Don Quijote de la Mancha

The author argues that Cervantes’s Don Quijote can be read in economic terms, and that it containslessons about the importance of political and monetary freedom. Through a detailed analysis of different episodes, the article presents the ways in which concepts such as Gresham’s Law, inflation, subjective value theory, price controls, and usury are depicted in the novel. Cervantes’s work shares much of the economic philosophy of the School of Salamanca, and this essay ultimately demonstrates that Don Quijote prompts readers to reflect on theproblems caused by economic practices that are directed against individual freedom.El autor sostiene que Don Quijote de Cervantes puede leerse en clave económica, y que contiene lecciones sobre la importancia de la libertad política y monetaria. A través de un análisis pormenorizado de distintos episodios de la obra, el artículo presenta el modo en que aparecen conceptos como la Ley de Gresham, la inflación, la teoría subjetiva del valor, el control de precios y la usura. La obra cervantina comparte la misma visión económica de la Escuela de Salamanca, y en última instancia este trabajo demuestra que Don Quijote busca mover a la reflexión sobre los problemas que ocasionan las prácticas económicas que se dirigen en contra de la libertad individual

Humanoid Mobile Manipulation Using Controller Refinement

An important class of mobile manipulation problems are move-to-grasp problems where a mobile robot must navigate to and pick up an object. One of the distinguishing features of this class of tasks is its coarse-to-fine structure. Near the beginning of the task, the robot can only sense the target object coarsely or indirectly and make gross motion toward the object. However, after the robot has located and approached the object, the robot must finely control its grasping contacts using precise visual and haptic feedback. In this paper, it is proposed that move-to-grasp problems are naturally solved by a sequence of controllers that iteratively refines what ultimately becomes the final solution. This paper introduces the notion of a refining sequence of controllers and characterizes this type of solution. The approach is demonstrated in a move-to-grasp task where Robonaut, the NASA/JSC dexterous humanoid, is mounted on a mobile base and navigates to and picks up a geological sample box. In a series of tests, it is shown that a refining sequence of controllers decreases variance in robot configuration relative to the sample box until a successful grasp has been achieved

DeepCell 2.0: Automated cloud deployment of deep learning models for large-scale cellular image analysis

Deep learning is transforming the ability of life scientists to extract information from images. While these techniques have superior accuracy in comparison to conventional approaches and enable previously impossible analyses, their unique hardware and software requirements have prevented widespread adoption by life scientists. To meet this need, we have developed DeepCell 2.0, an open source library for training and delivering deep learning models with cloud computing. This library enables users to configure and manage a cloud deployment of DeepCell 2.0 on all commonly used operating systems. Using single-cell segmentation as a use case, we show that users with suitable training data can train models and analyze data with those models through a web interface. We demonstrate that by matching analysis tasks with their hardware requirements, we can efficiently use computational resources in the cloud and scale those resources to meet demand, significantly reducing the time necessary for large-scale image analysis. By reducing the barriers to entry, this work will empower life scientists to apply deep learning methods to their data. A persistent deployment is available at http://www.deepcell.org