Speed-up via Quantum Sampling

The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether quantum computers can speed-up classical mixing processes based on Markov chains. To this end, we present a new quantum algorithm, making it possible to prepare a quantum sample, i.e., a coherent version of the stationary distribution of a reversible Markov chain. Our algorithm has a significantly better running time than that of a previous algorithm based on adiabatic state generation. We also show that our methods provide a speed-up over a recently proposed method for obtaining ground states of (classical) Hamiltonians.Comment: 8 pages, fixed some minor typo

Theory of the Quantum Speed Up

Insofar as quantum computation is faster than classical, it appears to be irreversible. In all quantum algorithms found so far the speed-up depends on the extra-dynamical irreversible projection representing quantum measurement. Quantum measurement performs a computation that dynamical computation cannot accomplish as efficiently.Comment: 10 pages, RevTex, 1 page of 3 figure

Augmented reality usage for prototyping speed up

The first part of the article describes our approach for solution of this problem by means of Augmented Reality. The merging of the real world model and digital objects allows streamline the work with the model and speed up the whole production phase significantly. The main advantage of augmented reality is the possibility of direct manipulation with the scene using a portable digital camera. Also adding digital objects into the scene could be done using identification markers placed on the surface of the model. Therefore it is not necessary to work with special input devices and lose the contact with the real world model. Adjustments are done directly on the model. The key problem of outlined solution is the ability of identification of an object within the camera picture and its replacement with the digital object. The second part of the article is focused especially on the identification of exact position and orientation of the marker within the picture. The identification marker is generalized into the triple of points which represents a general plane in space. There is discussed the space identification of these points and the description of representation of their position and orientation be means of transformation matrix. This matrix is used for rendering of the graphical objects (e. g. in OpenGL and Direct3D).Comment: Keywords: augmented reality, prototyping, pose estimation, transformation matri

Proposals which speed-up function-space MCMC

Inverse problems lend themselves naturally to a Bayesian formulation, in which the quantity of interest is a posterior distribution of state and/or parameters given some uncertain observations. For the common case in which the forward operator is smoothing, then the inverse problem is ill-posed. Well-posedness is imposed via regularisation in the form of a prior, which is often Gaussian. Under quite general conditions, it can be shown that the posterior is absolutely continuous with respect to the prior and it may be well-defined on function space in terms of its density with respect to the prior. In this case, by constructing a proposal for which the prior is invariant, one can define Metropolis-Hastings schemes for MCMC which are well-defined on function space, and hence do not degenerate as the dimension of the underlying quantity of interest increases to infinity, e.g. under mesh refinement when approximating PDE in finite dimensions. However, in practice, despite the attractive theoretical properties of the currently available schemes, they may still suffer from long correlation times, particularly if the data is very informative about some of the unknown parameters. In fact, in this case it may be the directions of the posterior which coincide with the (already known) prior which decorrelate the slowest. The information incorporated into the posterior through the data is often contained within some finite-dimensional subspace, in an appropriate basis, perhaps even one defined by eigenfunctions of the prior. We aim to exploit this fact and improve the mixing time of function-space MCMC by careful rescaling of the proposal. To this end, we introduce two new basic methods of increasing complexity, involving (i) characteristic function truncation of high frequencies and (ii) hessian information to interpolate between low and high frequencies

Job Combinations and Speed-up in Steel

[Excerpt] The Rail Mill Manning Agreement at South works in not unique. Reducing labor costs by combining jobs is a key part of the steel companies\u27 strategy for regaining profitability. MCLR has conducted a survey of five other mills to find out what the companies are doing to reduce the work force, and speed up work. We print here a summary of our preliminary findings