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Bernstein-Vazirani algorithm (the one-query algorithm) can identify a completely specified linear Boolean function using a single query to the oracle with certainty. The first aim of the paper is to show that if the provided Boolean…

Quantum Physics · Physics 2015-02-02 Ahmed Younes

We introduce a novel quantum algorithm for the lattice Boltzmann method (LBM) based on the one-step simplified LBM. The structure of the algorithm allows for more flexibility in modelling different physics in contrast to earlier quantum…

We described a simple algorithm running in linear time for each fixed constant $k$, that either establishes that the pathwidth of a graph $G$ is greater than $k$, or finds a path-decomposition of $G$ of width at most $O(2^{k})$. This…

Combinatorics · Mathematics 2009-09-25 Kevin Cattell , Michael J. Dinneen , Michael R. Fellows

This paper introduces a novel quantum algorithm that is able to classify a hierarchy of classes of imbalanced Boolean functions. The fundamental characteristic of imbalanced Boolean functions is that the proportion of elements in their…

We present a quantum algorithm for computing the period lattice of infrastructures of fixed dimension. The algorithm applies to infrastructures that satisfy certain conditions. The latter are always fulfilled for infrastructures obtained…

Quantum Physics · Physics 2012-06-13 Felix Fontein , Pawel Wocjan

We present a modification of Simon's algorithm that in some cases is able to fit experimentally obtained data to appropriately chosen trial functions with high probability. Modulo constants pertaining to the reliability and probability of…

Quantum Physics · Physics 2009-11-10 Darin Goldstein

Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution exponentially faster than classical algorithms in terms of…

Quantum Physics · Physics 2024-04-01 Zeguan Wu , Sidhant Misra , Tamás Terlaky , Xiu Yang , Marc Vuffray

Nonlinear boolean equation systems play an important role in a wide range of applications. Grover's algorithm is one of the best-known quantum search algorithms in solving the nonlinear boolean equation system on quantum computers. In this…

Quantum Physics · Physics 2024-10-16 Xiang Li , Hanxiang Shen , Weiguo Gao , Yingzhou Li

Quantum algorithms for solving noisy linear problems are reexamined, under the same assumptions taken from the existing literature. The findings of this work include on the one hand extended applicability of the quantum Fourier transform to…

Quantum Physics · Physics 2024-11-27 Minkyu Kim , Panjin Kim

We investigate quantum algorithms for classification, a fundamental problem in machine learning, with provable guarantees. Given $n$ $d$-dimensional data points, the state-of-the-art (and optimal) classical algorithm for training…

Quantum Physics · Physics 2019-05-28 Tongyang Li , Shouvanik Chakrabarti , Xiaodi Wu

A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for $D$-optimal criterion on continuous design spaces are…

Computation · Statistics 2018-04-10 Jiangtao Duan , Wei Gao , Hon Keung Tony Ng

The goal of this paper is to outline a general-purpose scalable implementation of Shor's period finding algorithm using fundamental quantum gates, and to act as a blueprint for linear optical implementations of Shor's algorithm for both…

Quantum Physics · Physics 2016-12-23 J. T. Davies , Christopher J. Rickerd , Mike A. Grimes , Durdu O. Guney

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…

Quantum Physics · Physics 2007-05-23 Subhamoy Maitra , Partha Mukhopadhyay

Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor's algorithm, sampling from the quantum Fourier spectrum is used to discover periodicity of the modular…

Quantum Physics · Physics 2015-05-14 Martin Roetteler

A novel polynomial expansion method of symmetric Boolean functions is described. The method is efficient for symmetric Boolean function with small set of valued numbers and has the linear complexity for elementary symmetric Boolean…

Discrete Mathematics · Computer Science 2013-06-25 Danila A. Gorodecky

The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an…

Quantum Physics · Physics 2009-11-10 Jérémie Roland , Nicolas J. Cerf

Quantum algorithms for factoring and discrete logarithm have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the possibility of extending this general viewpoint to finding hidden…

Quantum Physics · Physics 2015-06-02 Mark Ettinger , Peter Hoyer

We propose a quantum machine learning algorithm for efficiently solving a class of problems encoded in quantum controlled unitary operations. The central physical mechanism of the protocol is the iteration of a quantum time-delayed equation…

Simon's algorithm is a polynomial period-finding algorithm that has been used to exploit the algebraic structure of specific symmetric ciphers, showing that exponential speedups in their cryptanalysis are theoretically possible. While the…

Quantum Physics · Physics 2026-04-29 Anina Köhler , Jakob Murauer , Tim Heine , Stefan Rosemann , Tobias Hemmert

A fast algorithm is presented for determining the linear complexity and the minimal polynomial of periodic sequences over GF(q) with period q n p m, where p is a prime, q is a prime and a primitive root modulo p2. The algorithm presented…

Cryptography and Security · Computer Science 2007-05-23 Jianqin Zhou