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While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
Quantum computing enables the efficient resolution of complex problems, often outperforming classical methods across various applications. In 2009, Harrow, Hassidim and Lloyd proposed an algorithm for solving linear systems of equations,…
Quantum computers are known to provide an exponential advantage over classical computers for the solution of linear differential equations in high-dimensional spaces. Here, we present a quantum algorithm for the solution of nonlinear…
The application of quantum algorithms to classical problems is generally accompanied by significant bottlenecks when transferring data between quantum and classical states, often negating any intrinsic quantum advantage. Here we address…
Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…
Gaussian processes are widely known for their ability to provide probabilistic predictions in supervised machine learning models. Their non-parametric nature and flexibility make them particularly effective for regression tasks. However,…
For quantum computers to become useful tools to physicists, engineers and computational scientists, quantum algorithms for solving nonlinear differential equations need to be developed. Despite recent advances, the quest for a solver that…
Solving linear systems of equations plays a fundamental role in numerous computational problems from different fields of science. The widespread use of numerical methods to solve these systems motivates investigating the feasibility of…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
We develop a hybrid classical-quantum method for solving the Lorenz system. We use the forward Euler method to discretize the system in time, transforming it into a system of equations. This set of equations is solved using the Variational…
In computational fluid dynamics (CFD), the numerical integration of the Navier-Stokes equations is frequently constrained by the Poisson equation to determine the pressure. Discretization of this equation often results in the need to solve…
Partial differential equation solvers are required to solve the Navier-Stokes equations for fluid flow. Recently, algorithms have been proposed to simulate fluid dynamics on quantum computers. Fault-tolerant quantum devices might enable…
Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the…
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…
There are few approaches to the solution of a system of nonlinear differential equations in partial derivatives, for example $\cite{NK87} - \cite{EK98}$. In our paper we propose an approach that was used to solve the Navier-Stokes equations…
Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms for solving linear systems has been a significant…
Finding solutions to systems of linear equations is a common prob\-lem in many areas of science and engineering, with much potential for a speedup on quantum devices. While the Harrow-Hassidim-Lloyd (HHL) quantum algorithm yields up to an…
We present a systematic pathway for solving differential equations within the quantum linear systems framework by combining block encoding with Quantum Singular Value Transformation (QSVT). The approach is demonstrated on a complex…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
Solving linear systems is of great importance in numerous fields. Proposed quantum algorithms for preparing solutions for linear systems include the HHL algorithm with subsequent refinements and variational methods. Circulant linear systems…