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The discrete cosine transform (DCT) is the key step in many image and video coding standards. The 8-point DCT is an important special case, possessing several low-complexity approximations widely investigated. However, 16-point DCT…
In this research, we create a scalable version of the quantum Fourier transform-based arithmetic circuit to perform addition and subtraction operations on N n-bit unsigned integers encoded in quantum registers, and it is compatible with…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
Mitigating errors in computing and communication systems has seen a great deal of research since the beginning of the widespread use of these technologies. However, as we develop new methods to do computation or communication, we also need…
Applications of the three-dimensional transformation for rotating coordinate systems to quantum mechanics, general theory relativity and optics are considered.
The quantum Fourier transform (QFT) brings efficiency in many respects, especially usage of resource, for most operations on quantum computers. In this study, the existing QFT-based and non-QFT-based quantum arithmetic operations are…
In the presence of dynamic insertions and deletions into a partially reconfigurable FPGA, fragmentation is unavoidable. This poses the challenge of developing efficient approaches to dynamic defragmentation and reallocation. One key aspect…
Rotational computed laminography (CL) has broad application potential in three-dimensional imaging of plate-like objects, as it only needs x-ray to pass through the tested object in the thickness direction during the imaging process. In…
In this work, approximate eight-bit floating-point operations performed using simple integer operations is discussed. For two-bit mantissa formats, faithful rounding can always be obtained for the considered operations. For all operations,…
Symplectic numerical methods have become a widely-used choice for the accurate simulation of Hamiltonian systems in various fields, including celestial mechanics, molecular dynamics and robotics. Even though their characteristics are…
With its rich dynamics, the quantum harmonic oscillator is an innate platform for understanding real-world quantum systems and could even excel as the heart of a quantum computer. A particularly promising and rapidly advancing platform that…
We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our…
Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional…
The multisilce method is an important algorithm for electron diffraction and image simulations in transmission electron microscopy. We have proposed a quantum algorithm of the multislice method based on quantum circuit model previously. In…
Fast Fourier transform (FFT) of large number of samples requires huge hardware resources of field programmable gate arrays (FPGA), which needs more area and power. In this paper, we present an area efficient architecture of FFT processor…
Neural rendering techniques have made substantial progress in generating photo-realistic 3D scenes. The latest 3D Gaussian Splatting technique has achieved high quality novel view synthesis as well as fast rendering speed. However, 3D…
This paper proposes a systematic and novel component level co-rotational (CR) framework, for upgrading existing 3D continuum finite elements to flexible multibody analysis. Without using any model reduction techniques, the high efficiency…
The FFT of three-dimensional (3D) input data is an important computational kernel of numerical simulations and is widely used in High Performance Computing (HPC) codes running on a large number of processors. Performance of many scientific…
The software configurable processor finds best use in the embedded systems. These processors have onchip logic like FPGA (Field Programmable Gate Array) and thus can be configured to implement custom hardware functionality. The digital…
Recent research has focused on accelerating stencil computations by exploiting emerging hardware like Tensor Cores. To leverage these accelerators, the stencil operation must be transformed to matrix multiplications. However, this…