Related papers: Randomization Using Quasigroups, Hadamard and Numb…
Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By leveraging and extending recent results from random matrix…
In this paper we study a one-dimensional quantum random walk with the Hadamard transformation which is often called the Hadamard walk. We construct the Hadamard walk using a transition matrix on probability amplitude and give some results…
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…
Efficient methods for generating pseudo-randomly distributed unitary operators are needed for the practical application of Haar distributed random operators in quantum communication and noise estimation protocols. We develop a theoretical…
In this work we have considered formal power series and partial differential equations, and their relationship with Coding Theory. We have obtained the nature of solutions for the partial differential equations for Cycle Poisson Case. The…
In this paper, we propose a quasigroup based block cipher design. The round functions of the encryption and decryption algorithms use quasigroup based string transformations. We show the robustness of the design against the standard…
Previously, the author introduced quasirandom permutations, permutations of $\mathbb{Z}_n$ which map intervals to sets with low discrepancy. Here we show that several natural number-theoretic permutations are quasirandom, some very strongly…
Complex extension of quantum mechanics and the discovery of pseudo-unitarily invariant random matrix theory has set the stage for a number of applications of these concepts in physics. We briefly review the basic ideas and present…
In this paper we introduce activation functions that move the entire computation of Convolutional Networks into the frequency domain, where they are actually Hadamard Networks. To achieve this result we employ the properties of Discrete…
Randomized Hadamard Transforms (RHTs) have emerged as a computationally efficient alternative to the use of dense unstructured random matrices across a range of domains in computer science and machine learning. For several applications such…
This paper investigates the effect of permutations on blocks of a prime reciprocal sequence on its randomness. A relationship between the number of permutations used and the improvement of performance is presented. This can be used as a…
We describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application we use our algorithms to enumerate all transformation…
This is a presentation of recent work on quantum permutation groups. Contains: a short introduction to operator algebras and Hopf algebras; quantum permutation groups, and their basic properties; diagrams, integration formulae, asymptotic…
Transition amplitudes and transition probabilities are relevant to many areas of physics simulation, including the calculation of response properties and correlation functions. These quantities can also be related to solving linear systems…
Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum…
Quantum mechanics requires the operation of quantum computers to be unitary, and thus makes it important to have general techniques for developing fast quantum algorithms for computing unitary transforms. A quantum routine for computing a…
We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of…
We introduce the quantum fractional Hadamard transform with continuous variables. It is found that the corresponding quantum fractional Hadamard operator can be decomposed into a single-mode fractional operator and two single-mode squeezing…
Entangled multipartite states are resources for universal quantum computation, but they can also give rise to ensembles of unitary transformations, a topic usually studied in the context of random quantum circuits. Using several graph state…
We present a hybrid quantum-classical framework for simulating generic matrix functions more amenable to early fault-tolerant quantum hardware than standard quantum singular-value transformations. The method is based on randomization over…