Layered architecture for quantum computing

We develop a layered quantum computer architecture, which is a systematic framework for tackling the individual challenges of developing a quantum computer while constructing a cohesive device design. We discuss many of the prominent techniques for implementing circuit-model quantum computing and introduce several new methods, with an emphasis on employing surface code quantum error correction. In doing so, we propose a new quantum computer architecture based on optical control of quantum dots. The timescales of physical hardware operations and logical, error-corrected quantum gates differ by several orders of magnitude. By dividing functionality into layers, we can design and analyze subsystems independently, demonstrating the value of our layered architectural approach. Using this concrete hardware platform, we provide resource analysis for executing fault-tolerant quantum algorithms for integer factoring and quantum simulation, finding that the quantum dot architecture we study could solve such problems on the timescale of days.Comment: 27 pages, 20 figure

A TMS DSP processor based case study of Grigoryan FFT performance over Cooley-Tukey FFT (TMS320C6748, TMS320C5515)

Abstract:-Frequency analysis plays vital role in the applications like cryptanalysis, steganalysi

Data hiding in multimedia - theory and applications

Multimedia data hiding or steganography is a means of communication using subliminal channels. The resource for the subliminal communication scheme is the distortion of the original content that can be tolerated. This thesis addresses two main issues of steganographic communication schemes: 1. How does one maximize the distortion introduced without affecting fidelity of the content? 2. How does one efficiently utilize the resource (the distortion introduced) for communicating as many bits of information as possible? In other words, what is a good signaling strategy for the subliminal communication scheme? Close to optimal solutions for both issues are analyzed. Many techniques for the issue for maximizing the resource, viz, the distortion introduced imperceptibly in images and video frames, are proposed. Different signaling strategies for steganographic communication are explored, and a novel signaling technique employing a floating signal constellation is proposed. Algorithms for optimal choices of the parameters of the signaling technique are presented. Other application specific issues like the type of robustness needed are taken into consideration along with the established theoretical background to design optimal data hiding schemes. In particular, two very important applications of data hiding are addressed - data hiding for multimedia content delivery, and data hiding for watermarking (for proving ownership). A robust watermarking protocol for unambiguous resolution of ownership is proposed

Image Enhancement by Elliptic Discrete Fourier Transforms

This paper describes a method of enhancement of grayscale and color image in the frequency domain by the pair of two elliptic discrete Fourier transforms (EDFT). Unlike the traditional discrete Fourier transform (DFT), the EDFT is parameterized and the parameter defines ellipses (not circles) around which the input data are rotated. Methods of the traditional DFT are widely used in image enhancement, and the transform rotates data of images around the circles. The presented method of image enhancement proposes processing images on different set of ellipses for the direct and inverse transforms. Our preliminary experimental examples show effectiveness of the proposed method. The Illustrative examples of image enhancement are given

Half-tapering strategy for conditional simulation with large datasets

Gaussian conditional realizations are routinely used for risk assessment and planning in a variety of Earth sciences applications. Conditional realizations can be obtained by first creating unconditional realizations that are then post-conditioned by kriging. Many efficient algorithms are available for the first step, so the bottleneck resides in the second step. Instead of doing the conditional simulations with the desired covariance (F approach) or with a tapered covariance (T approach), we propose to use the taper covariance only in the conditioning step (Half-Taper or HT approach). This enables to speed up the computations and to reduce memory requirements for the conditioning step but also to keep the right short scale variations in the realizations. A criterion based on mean square error of the simulation is derived to help anticipate the similarity of HT to F. Moreover, an index is used to predict the sparsity of the kriging matrix for the conditioning step. Some guides for the choice of the taper function are discussed. The distributions of a series of 1D, 2D and 3D scalar response functions are compared for F, T and HT approaches. The distributions obtained indicate a much better similarity to F with HT than with T.Comment: 39 pages, 2 Tables and 11 Figure

Adjoint-based mixing enhancement for binary fluids

Mixing is a fundamental fluid process that dominates {a} great many natural phenomena and is present in a wide variety of industrial applications. Therefore, studying the characteristics and optimisation of this process may lead to a significant impact in many fields. This thesis presents an analytical and computational framework for optimising fluid mixing processes using embedded stirrers based on a non-linear direct-adjoint looping approach. The governing equations are the non-linear Navier-Stokes equations, augmented by an evolution equation for a passive scalar, which are solved by a Fourier-based spectral method. Stirrers are embedded in the computational domain by a Brinkman-penalisation technique, and shape and path gradients for the stirrers are computed from the adjoint solution. The relationship between this penalisation approach and the adjoint will be examined through the derivation of a dual system of equations, and three different optimisation scenarios of increasing complexity, each focusing on different optimisation parameters, are considered. Within the limits of the parameterisations of the geometry and the externally imposed bounds, significant improvements in mixing efficiency are achieved in all cases.Open Acces

Progressive transmission and display of static images

Progressive image transmission has been studied for some time in association with image displays connected to remote image sources, by communications channels of insufficient data rate to give subjectively near instantaneous transmission. Part of the work presented in this thesis addresses the progressive transmission problem constrained that the final displayed image is exactly identical to the source image with no redundant data transmitted. The remainder of the work presented is concerned with producing the subjectively best image for display from the information transmitted throughout the progression. Quad-tree and binary-tree based progressive transmission techniques are reviewed, especially an exactly invertible table based binary-tree technique. An algorithm is presented that replaces the table look-up in this technique, typically reducing implementation cost, and results are presented for the subjective improvement using interpolation of the display images. The relevance of the interpolation technique to focusing the progressive sequence on some part of the image is also discussed. Some aspects of transform coding for progressive transmission are reviewed, intermediate image resolution and most importantly problems associated with the coding being exactly invertible. Starting with the two-dimensional case, an algorithm is developed, that judged by the progressive display image can mimic the behaviour of a linear transform while also being exactly invertible (no quantisation). This leads to a mean/difference transform similar to the binary-tree technique. The mimic algorithm is developed to operate on n-dimensions and used to mimic an eight-dimensional cosine transform. Photographic and numerical results of the application of this algorithm to image data are presented. An area transform, interpolation to disguise block boundaries and bit allocation to coefficients, based on the cosine mimic transform are developed and results presented