Related papers: Quantum relaxed row and column iteration methods b…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
Quantum machine learning techniques have been proposed as a way to potentially enhance performance in machine learning applications. In this paper, we introduce two new quantum methods for neural networks. The first one is a quantum…
Deterministic and randomized, row-action and column-action linear solvers have become increasingly popular owing to their simplicity, low computational and memory complexities, and ease of composition with other techniques. Moreover, in…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
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…
Near term quantum computers suffer from the presence of different noise sources. In order to mitigate for this effect and acquire results with significantly better accuracy, there is the urge of designing efficient error correction or error…
Quantum algorithms have been widely studied in the context of combinatorial optimization problems. While this endeavor can often analytically and practically achieve quadratic speedups, theoretical and numeric studies remain limited,…
Engineering design processes involve iterative design evaluations requiring numerous computationally intensive numerical simulations. Quantum algorithms promise substantial speedups for specific tasks relevant to engineering simulations.…
This paper discusses the compilation, optimization, and error mitigation of quantum algorithms, essential steps to execute real-world quantum algorithms. Quantum algorithms running on a hybrid platform with QPU and CPU/GPU take advantage of…
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…
Based on the column pivoted QR decomposition, we propose some randomized algorithms including pass-efficient ones for the generalized CUR decompositions of matrix pair and matrix triplet. Detailed error analyses of these algorithms are…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…
Harrow, Hassidim, and Lloyd showed that for a suitably specified $N \times N$ matrix $A$ and $N$-dimensional vector $\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of…
Presented here is a matrix inversion method utilizing quantum searching algorithm. In this method, huge Hilbert space as a whole spanned by myriad of eigen states is searched and evaluated efficiently by sequential reduction in dimension…
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…
Major obstacles remain to the implementation of macroscopic quantum computing: hardware problems of noise, decoherence, and scaling; software problems of error correction; and, most important, algorithm construction. Finding truly quantum…
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…
Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that…
Quantum computers can solve specific complex tasks for which no reasonable-time classical algorithm is known. Quantum computers do however also offer inherent security of data, as measurements destroy quantum states. Using shared entangled…
We propose and implement a family of quantum-informed recursive optimization (QIRO) algorithms for combinatorial optimization problems. Our approach leverages quantum resources to obtain information that is used in problem-specific…