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In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
The Bregman-Kaczmarz method is an iterative method which can solve strongly convex problems with linear constraints and uses only one or a selected number of rows of the system matrix in each iteration, thereby making it amenable for…
Identifying computational tasks suitable for (future) quantum computers is an active field of research. Here we explore utilizing quantum computers for the purpose of solving differential equations. We consider two approaches: (i) basis…
Quantum machine learning has the potential for broad industrial applications, and the development of quantum algorithms for improving the performance of neural networks is of particular interest given the central role they play in machine…
The complexity of matrix multiplication is a central topic in computer science. While the focus has traditionally been on exact algorithms, a long line of literature also considers randomized algorithms, which return an approximate solution…
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…
Many quantum algorithms for numerical linear algebra assume black-box access to a block-encoding of the matrix of interest, which is a strong assumption when the matrix is not sparse. Kernel matrices, which arise from discretizing a kernel…
Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. [Suba\c{s}i et al., Phys. Rev. Lett.…
We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…
We review the basic outline of the highly successful diffusion Monte Carlo technique commonly used in contexts ranging from electronic structure calculations to rare event simulation and data assimilation, and propose a new class of…
Optical computing harnesses the speed of light to perform vector-matrix operations efficiently. It leverages interference, a cornerstone of quantum computing algorithms, to enable parallel computations. In this work, we interweave quantum…
The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether…
The randomized Kaczmarz ($\RK$) algorithm is a simple but powerful approach for solving consistent linear systems $Ax=b$. This paper proposes an accelerated randomized Kaczmarz ($\ARK$) algorithm with better convergence than the standard…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
Nonlinear equations are challenging to solve due to their inherently nonlinear nature. As analytical solutions typically do not exist, numerical methods have been developed to tackle their solutions. In this article, we give a quantum…
Quantum computers use quantum resources to carry out computational tasks and may outperform classical computers in solving certain computational problems. Special-purpose quantum computers such as quantum annealers employ quantum adiabatic…
A novel quantum algorithm for solving the Boltzmann-Maxwell equations of the 6D collisionless plasma is proposed. The equation describes the kinetic behavior of plasma particles in electromagnetic fields and is known for the classical…
Quantum simulation is known to be capable of simulating certain dynamical systems in continuous time -- Schrodinger's equations being the most direct and well-known -- more efficiently than classical simulation. Any linear dynamical system…
While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…
Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key…