Related papers: Solving Linear Systems of Equations with the Quant…
Although the Harrow-Hassidim-Lloyd (HHL) algorithm offers an exponential speedup in system size for treating linear equations of the form $A\vec{x}=\vec{b}$ on quantum computers when compared to their traditional counterparts, it faces a…
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…
The goal of the load flow study is to ensure that electrical power is delivered efficiently and reliably to end-users while maintaining the stability and security of the power system. Newton-Raphson is a numerical method used widely for…
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…
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…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
There has been significant progress in the development of quantum algorithms for solving linear systems of equations with a growing body of applications to Computational Fluid Dynamics (CFD) and CFD-like problems. This work extends previous…
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…
Power flow calculation plays an important role in planning, operation, and control of the power system. The quantum HHL algorithm can achieve theoretical exponential speedup over classical algorithms on DC power flow calculation. Since the…
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…
Practical quantum computing applications to power grids are nonexistent at the moment. This paper investigates how a fundamental grid problem, namely DC power flow, can be solved using quantum computing. Power flow is the most widely used…
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…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
We analyze the performance of the Harrow-Hassidim-Lloyd algorithm (HHL algorithm) for solving linear problems and of a variant of this algorithm (HHL variant) commonly encountered in literature. This variant relieves the algorithm of…
In this exploratory numerical study, we assess the suitability of Quantum Linear Solvers(QLSs)toward providing a quantum advantage for Networks-based Linear System Problems (NLSPs). NLSPs naturally arise from graphs, and are of importance…
Though quantum algorithm acts as an important role in quantum computation science, not only for providing a great vision for solving classically unsolvable problems, but also due to the fact that it gives a potential way of understanding…
Conventional classical solvers are commonly used for solving matrix equation systems resulting from the discretization of SIEs in computational electromagnetics (CEM). However, the memory requirement would become a bottleneck for classical…
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…
Quantum computing is evolving so rapidly that it forces us to revisit, rewrite, and update the foundations of the theory. \emph{Basic Quantum Algorithms} revisits the earliest quantum algorithms. The journey began in 1985 with Deutsch…