Tractable Simulation of Error Correction with Honest Approximations to Realistic Fault Models

In previous work, we proposed a method for leveraging efficient classical simulation algorithms to aid in the analysis of large-scale fault tolerant circuits implemented on hypothetical quantum information processors. Here, we extend those results by numerically studying the efficacy of this proposal as a tool for understanding the performance of an error-correction gadget implemented with fault models derived from physical simulations. Our approach is to approximate the arbitrary error maps that arise from realistic physical models with errors that are amenable to a particular classical simulation algorithm in an "honest" way; that is, such that we do not underestimate the faults introduced by our physical models. In all cases, our approximations provide an "honest representation" of the performance of the circuit composed of the original errors. This numerical evidence supports the use of our method as a way to understand the feasibility of an implementation of quantum information processing given a characterization of the underlying physical processes in experimentally accessible examples.Comment: 34 pages, 9 tables, 4 figure

Sequential non-rigid structure from motion using physical priors

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.We propose a new approach to simultaneously recover camera pose and 3D shape of non-rigid and potentially extensible surfaces from a monocular image sequence. For this purpose, we make use of the Extended Kalman Filter based Simultaneous Localization And Mapping (EKF-SLAM) formulation, a Bayesian optimization framework traditionally used in mobile robotics for estimating camera pose and reconstructing rigid scenarios. In order to extend the problem to a deformable domain we represent the object's surface mechanics by means of Navier's equations, which are solved using a Finite Element Method (FEM). With these main ingredients, we can further model the material's stretching, allowing us to go a step further than most of current techniques, typically constrained to surfaces undergoing isometric deformations. We extensively validate our approach in both real and synthetic experiments, and demonstrate its advantages with respect to competing methods. More specifically, we show that besides simultaneously retrieving camera pose and non-rigid shape, our approach is adequate for both isometric and extensible surfaces, does not require neither batch processing all the frames nor tracking points over the whole sequence and runs at several frames per second.Peer ReviewedPostprint (author's final draft

SIGGRAPH

We present a method for recovering a temporally coherent, deforming triangle mesh with arbitrarily changing topology from an incoherent sequence of static closed surfaces. We solve this problem using the surface geometry alone, without any prior information like surface templates or velocity fields. Our system combines a proven strategy for triangle mesh improvement, a robust multi-resolution non-rigid registration routine, and a reliable technique for changing surface mesh topology. We also introduce a novel topological constraint enforcement algorithm to ensure that the output and input always have similar topology. We apply our technique to a series of diverse input data from video reconstructions, physics simulations, and artistic morphs. The structured output of our algorithm allows us to efficiently track information like colors and displacement maps, recover velocity information, and solve PDEs on the mesh as a post process

Deformable Simplicial Complexes

In this dissertation we present a novel method for deformable interface tracking in 2D and 3D|deformable simplicial complexes (DSC). Deformable interfaces are used in several applications, such as fluid simulation, image analysis, reconstruction or structural optimization. In the DSC method, the interface (curve in 2D; surface in 3D) is represented explicitly as a piecewise linear curve or surface. However, the domain is also subject to discretization: triangulation in 2D; tetrahedralization in 3D. This way, the interface can be alternatively represented as a set of edges/triangles separating triangles/tetrahedra marked as outside from those marked as inside. Such an approach allows for robust topological adaptivity. Among other advantages of the deformable simplicial complexes there are: space adaptivity, ability to handle and preserve sharp features, possibility for topology control. We demonstrate those strengths in several applications. In particular, a novel, DSC-based fluid dynamics solver has been developed during the PhD project. A special feature of this solver is that due to the fact that DSC maintains an explicit interface representation, surface tension is more easily dealt with. One particular advantage of DSC is the fact that as an alternative to topology adaptivity, topology control is also possible. This is exploited in the construction of cut loci on tori where a front expands from a single point on a torus and stops when it self-intersects

IST Austria Thesis

Computer graphics is an extremely exciting field for two reasons. On the one hand, there is a healthy injection of pragmatism coming from the visual effects industry that want robust algorithms that work so they can produce results at an increasingly frantic pace. On the other hand, they must always try to push the envelope and achieve the impossible to wow their audiences in the next blockbuster, which means that the industry has not succumb to conservatism, and there is plenty of room to try out new and crazy ideas if there is a chance that it will pan into something useful. Water simulation has been in visual effects for decades, however it still remains extremely challenging because of its high computational cost and difficult artdirectability. The work in this thesis tries to address some of these difficulties. Specifically, we make the following three novel contributions to the state-of-the-art in water simulation for visual effects. First, we develop the first algorithm that can convert any sequence of closed surfaces in time into a moving triangle mesh. State-of-the-art methods at the time could only handle surfaces with fixed connectivity, but we are the first to be able to handle surfaces that merge and split apart. This is important for water simulation practitioners, because it allows them to convert splashy water surfaces extracted from particles or simulated using grid-based level sets into triangle meshes that can be either textured and enhanced with extra surface dynamics as a post-process. We also apply our algorithm to other phenomena that merge and split apart, such as morphs and noisy reconstructions of human performances. Second, we formulate a surface-based energy that measures the deviation of a water surface froma physically valid state. Such discrepancies arise when there is a mismatch in the degrees of freedom between the water surface and the underlying physics solver. This commonly happens when practitioners use a moving triangle mesh with a grid-based physics solver, or when high-resolution grid-based surfaces are combined with low-resolution physics. Following the direction of steepest descent on our surface-based energy, we can either smooth these artifacts or turn them into high-resolution waves by interpreting the energy as a physical potential. Third, we extend state-of-the-art techniques in non-reflecting boundaries to handle spatially and time-varying background flows. This allows a novel new workflow where practitioners can re-simulate part of an existing simulation, such as removing a solid obstacle, adding a new splash or locally changing the resolution. Such changes can easily lead to new waves in the re-simulated region that would reflect off of the new simulation boundary, effectively ruining the illusion of a seamless simulation boundary between the existing and new simulations. Our non-reflecting boundaries makes sure that such waves are absorbed