Related papers: Improved quantum algorithms for linear and nonline…
Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…
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…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
We present a novel variational quantum framework for nonlinear partial differential equation (PDE) constrained optimization problems. The proposed work extends the recently introduced bi-level variational quantum PDE constrained…
We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an $N\times N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\textbf{\emph{b}}$, and an initial vector $\textbf{\emph{x}}(0)$,…
Matrix scaling and matrix balancing are two basic linear-algebraic problems with a wide variety of applications, such as approximating the permanent, and pre-conditioning linear systems to make them more numerically stable. We study the…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…
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,…
A diffusion probabilistic model (DPM) is a generative model renowned for its ability to produce high-quality outputs in tasks such as image and audio generation. However, training DPMs on large, high-dimensional datasets such as…
We construct quantum algorithms to compute the solution and/or physical observables of nonlinear ordinary differential equations (ODEs) and nonlinear Hamilton-Jacobi equations (HJE) via linear representations or exact mappings between…
In this set of papers we formulate a stand alone method to derive maximal number of linearizing transformations for nonlinear ordinary differential equations (ODEs) of any order including coupled ones from a knowledge of fewer number of…
We develop a pivot-shifted Carleman linearization framework for quantum algorithms solving quadratic nonlinear ordinary differential equations. By shifting the dynamics by a pivot state prior to Carleman lifting, and combining this with a…
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…
This study examines the potential for fault-tolerant quantum computers to provide utility in fluid dynamics simulations, with a focus on drag force calculations for ship hull design. We assess whether quantum algorithms can surpass…
Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
We construct quantum algorithms to compute physical observables of nonlinear PDEs with M initial data. Based on an exact mapping between nonlinear and linear PDEs using the level set method, these new quantum algorithms for nonlinear…
The Harrow, Hassidim, Lloyd (HHL) algorithm is a quantum algorithm expected to accelerate solving large-scale linear ordinary differential equations (ODEs). To apply the HHL to non-linear problems such as chemical reactions, the system must…