Related papers: Alternative Numerical Techniques
The Number Theoretic Transform (NTT) can be regarded as a variant of the Discrete Fourier Transform. NTT has been quite a powerful mathematical tool in developing Post-Quantum Cryptography and Homomorphic Encryption. The Fourier Transform…
Quantum Image Processing is a recent highlight in the quantum computing field. All previous methods for representing the images as quantum states were defined using qubits. One Quantum Image Representation (QIR) method using qutrits is…
This paper is devoted to establishing several new formulas relating Bernoulli and Stirling numbers of both kinds.
I present a few new and recent ideas of the multiloop calculations.
Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developped in two spacetime dimensions, where many rigorous constructions are possible, as well as some complete…
I propose a new mathematical form for the quantum theory of gravity coupled to matter. The motivation is from the connection between CSW TQFT and the Ashtekar variables. I also connect the algebraic structure of TQFT with some thoughts…
Two new identities about Catalan numbers are treated with Zeilberger's algorithm and Watson's hypergeometric series evaluation.
We present some basic integer arithmetic quantum circuits, such as adders and multipliers-accumulators of various forms, as well as diagonal operators, which operate on multilevel qudits. The integers to be processed are represented in an…
In the paper, we consider quantum circuits for the Quantum Fourier Transform (QFT) algorithm. The QFT algorithm is a very popular technique used in many quantum algorithms. We present a generic method for constructing quantum circuits for…
Two different strategies of the relativistic quantum theory construction are considered and evaluated. The first strategy is the conventional strategy, based on application of the quantum mechanics technique to relativistic systems. This…
Non-uniform fast Fourier Transform (NUFFT) and inverse NUFFT (INUFFT) algorithms, based on the Fast Multipole Method (FMM) are developed and tested. Our algorithms are based on a novel factorization of the FFT kernel, and are implemented…
Algorithms for processing data in short-time batches are critical for both online and offline processing of streamed and large data respectively due to the quadratic relation between signal length and computational cost of convolution-based…
This paper presents 10-point and 12-point versions of the recently introduced number theoretic Hilbert (NHT) transforms. Such transforms have applications in signal processing and scrambling. Polymorphic solutions with respect to different…
To each local field (including the real or complex numbers) we associate a quantum dilogarithm and show that it satisfies a pentagon identity and some symmetries. Using an angled version of these quantum dilogarithms, we construct three…
In this paper, we introduce a novel quantum algorithm for the factorization of composite odd numbers. This work makes two significant contributions. First, we present a new improvement to the classical Fermat method, fourfold reducing the…
Quantum Process Tomography (QPT) methods aim at identifying, i.e. estimating, a given quantum process. QPT is a major quantum information processing tool, since it especially allows one to characterize the actual behavior of quantum gates,…
In this talk, we give a glimpse of the problems with quantum gravity and some possible solutions.
A new method of numerical solution for partial differential equations is proposed. The method is based on a fast matrix multiplication algorithm. Two-dimensional Poison equation is used for comparison of the proposed method with…
We present fast and highly parallelized versions of Shor's algorithm. With a sizable quantum computer it would then be possible to factor numbers with millions of digits. The main algorithm presented here uses FFT-based fast integer…
We consider the relations between well-known Fourier transform algorithms.