Related papers: Randomization Using Quasigroups, Hadamard and Numb…
This article presents a new class of Pseudorandom Number Generators. The generators are based on traversing a n-cube where a Balanced Hamiltonian Cycle has been removed. The construction of such generators is automatic for small number of…
A new model that maps a quantum random walk described by a Hadamard operator to a particular case of a random walk is presented. The model is represented by a Markov chain with a stochastic matrix, i.e., all the transition rates are…
Although quantum random number generators rely on the inherent indeterminism of quantum mechanics, ensuring that the numbers produced are secure remains a significant challenge. We introduce two semi-device-independent randomness expansion…
Quantum computing (QC) holds the promise of revolutionizing problem-solving by exploiting quantum phenomena like superposition and entanglement. It offers exponential speed-ups across various domains, from machine learning and security to…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
In this paper, we prove an important cryptographic property of $PE$-transformation proposed elsewhere. If $PE$-transformation is used as encrypting function then after $n$ applications of it on arbitrary message the distribution of…
Hadamard spectroscopy has earlier been used to speed-up multi-dimensional NMR experiments. In this work we speed-up the two-dimensional quantum computing scheme, by using Hadamard spectroscopy in the indirect dimension, resulting in a…
We review approaches to statistical inference based on randomization. Permutation tests are treated as an important special case. Under a certain group invariance property, referred to as the ``randomization hypothesis,'' randomization…
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…
This thesis discusses the young fields of quantum pseudo-randomness and quantum learning algorithms. We present techniques for derandomising algorithms to decrease randomness resource requirements and improve efficiency. One key object in…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
We introduce a new, elementary method for studying random differences in arithmetic progressions and convergence phenomena along random sequences of integers. We apply our method to obtain significant improvements on previously known…
We propose a novel quantum approach to signal processing, including a quantum algorithm for low-pass and high-pass filtering, based on the sequency-ordered Walsh-Hadamard transform. We present quantum circuits for performing the…
Quantum pseudorandomness, also known as unitary designs, comprise a powerful resource for quantum computation and quantum engineering. While it is known in theory that pseudorandom unitary operators can be constructed efficiently, realizing…
Random numbers play a crucial role in science and industry. Many numerical methods require the use of random numbers, in particular the Monte Carlo method. Therefore it is of paramount importance to have efficient random number generators.…
Quantum pseudorandomness has found applications in many areas of quantum information, ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum systems, and, more recently, in the foundations of quantum…
A new iterative low complexity algorithm has been presented for computing the Walsh-Hadamard transform (WHT) of an $N$ dimensional signal with a $K$-sparse WHT, where $N$ is a power of two and $K = O(N^\alpha)$, scales sub-linearly in $N$…
The structure of transformation semigroups on a finite set is analyzed by introducing a hierarchy of functions mapping subsets to subsets. The resulting hierarchy of semigroups has a corresponding hierarchy of minimal ideals, or kernels.…
A fast quantum search algorithm for continuous variables is presented. The result is the quantum continuous variable analog of Grover's algorithm originally proposed for qubits. A continuous variable analog of the Hadamard (i.e., Fourier…
Several cryptographic protocols constructed based on less-known algorithmic problems, such as those in non-commutative groups, group rings, semigroups, etc., which claim quantum security, have been broken through classical reduction methods…