Related papers: Quantum and Randomised Algorithms for Non-linearit…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
The study of non-linearity (linearity) of Boolean function was initiated by Rothaus in 1976. The classical non-linearity of a Boolean function is the minimum Hamming distance of its truth table to that of affine functions. In this note we…
An approximation to the solution of a stochastic parabolic equation is constructed using the Galerkin approximation followed by the Wiener Chaos decomposition. The result is applied to the nonlinear filtering problem for the time…
For cryptographic systems the method of confusion and diffusion is used as a fundamental technique to achieve security. Confusion is reflected in nonlinearity of certain Boolean functions describing the cryptographic transformation. In this…
Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship between the response variable and observed…
Solving a quadratic nonlinear system of equations (QNSE) is a fundamental, but important, task in nonlinear science. We propose an efficient quantum algorithm for solving $n$-dimensional QNSE. Our algorithm embeds QNSE into a…
The solution of large systems of nonlinear differential equations is needed for many applications in science and engineering. In this study, we present three main improvements to existing quantum algorithms based on the Carleman…
Quantum algorithms manipulate the amplitudes of quantum states to find solutions to computational problems. In this work, we present a framework for applying a general class of non-linear functions to the amplitudes of quantum states, with…
We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using postselection. We show that the minimal degree of the former equals (up to a…
The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…
Linear regression is a popular machine learning approach to learn and predict real valued outputs or dependent variables from independent variables or features. In many real world problems, its beneficial to perform sparse linear regression…
It is presently shown that the Deutsch-Jozsa algorithm is connected to the concept of bent function. Particularly, it is noticeable that the quantum circuit used to denote the well known quantum algorithm is by itself the quantum computer…
Starting from a generic generally covariant classical theory we introduce the logarithmic correction to the quantum wave equation. We demonstrate the emergence of the evolution time from the group of automorphisms of the von Neumann algebra…
Realist, no-collapse interpretations of quantum mechanics, such as Everett's, face the probability problem: how to justify the norm-squared (Born) rule from the wavefunction alone. While any basis-independent measure can only be…
We consider the problem of minimizing a continuous function given quantum access to a stochastic gradient oracle. We provide two new methods for the special case of minimizing a Lipschitz convex function. Each method obtains a dimension…
We give a new upper bound on the quantum query complexity of deciding $st$-connectivity on certain classes of planar graphs, and show the bound is sometimes exponentially better than previous results. We then show Boolean formula evaluation…
We consider deterministic and {\em randomized} quantum algorithms simulating $e^{-iHt}$ by a product of unitary operators $e^{-iA_jt_j}$, $j=1,...,N$, where $A_j\in\{H_1,...,H_m\}$, $H=\sum_{i=1}^m H_i$ and $t_j > 0$ for every $j$.…
Derandomization is the process of taking a randomized algorithm and turning it into a deterministic algorithm, which has attracted great attention in classical computing. In quantum computing, it is challenging and intriguing to derandomize…
Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from…
Boolean functions are important building blocks in cryptography for their wide application in both stream and block cipher systems. For cryptanalysis of such systems one tries to find out linear functions that are correlated to the Boolean…