相关论文: Alternative Numerical Techniques
New results on comparison of distributions of Gaussian quadratic forms are presented
Truncated Fourier Transforms (TFTs), first introduced by Van der Hoeven, refer to a family of algorithms that attempt to smooth "jumps" in complexity exhibited by FFT algorithms. We present an in-place TFT whose time complexity, measured in…
With the help of a new program, we do computations concerning the Witten-Reshetikhin-Turaev representations of mapping class groups. In particular we distinguish some mutant fibered knots. The program can be downloaded from…
The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route towards a numerical…
A New Number Theoretic Transform(NTT), which is a form of FFT, is introduced, that is faster than FFTs. Also, a multiplication algorithm is introduced that uses this to perform integer multiplication faster than O(n log n). It uses…
This paper creates and analyses a new quantum algorithm called the Amplified Quantum Fourier Transform (Amplified-QFT) for solving the following problem: The Local Period Problem: Let L = {0,1...N-1} be a set of N labels and let A be a…
We introduce two methods for quantum process and detector tomography. In the quantum process tomography method, we develop an analytical procedure for projecting the linear inversion estimation of a quantum channel onto the set of…
We propose an implementation of the algorithm for the fast Fourier transform (FFT) as a quantum circuit consisting of a combination of some quantum gates. In our implementation, a data sequence is expressed by a tensor product of vector…
The discrete Fourier transform and the FFT algorithm are extended from the circle to continuous graphs with equal edge lengths.
Two $(p,q)$-Laplace transforms are introduced and their relative properties are stated and proved. Applications are made to solve some $(p,q)$-linear difference equations.
Quantum machine learning techniques have been proposed as a way to potentially enhance performance in machine learning applications. In this paper, we introduce two new quantum methods for neural networks. The first one is a quantum…
We improve previous estimates for matrices belonging to the quantum annulus or to the numerical annulus.
We present here two new techniques to solve the one-dimensional random flight. The first one is an expansion in the number of collisions. The second one is the obtention of a Fourier series. This second technique can be applied to an…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
We introduce new rounding methods to improve the accuracy of finite precision quantum arithmetic. These quantum rounding methods are applicable when multiple samples are being taken from a quantum program. We show how to use multiple…
In this paper, two quantum networks for the addition operation are presented. One is the Modified Quantum Plain (MQP) adder, and the other is the Quantum Carry Look-Ahead (QCLA) adder. The MQP adder is obtained by modifying the Conventional…
A brief survey of recent results in the study of boundary integrable quantum field theories, indicating some currently open problems. Based on lectures given at the 2000 Eotvos Summer School in Physics on `Nonperturbative QFT methods and…
We present illustrations which show the usefulness of algebraic QFT. In particular in low-dimensional QFT, when Lagrangian quantization does not exist or is useless (e.g. in chiral conformal theories), the algebraic method is beginning to…
The article is devoted to new mathematical methods for psychophysical filtering of experimental data and their processing.
Different authors have done analysis regarding sums of powers References number 1,2 and 3, but systematic approach for solving Diophantine equations having sums of many biquadratics equal to a quartic has not been done before. In this paper…