Related papers: Solving 1D Poisson problem with a Variational Quan…
Discretizing Helmholtz problems via finite elements yields linear systems whose efficient solution remains a major challenge for classical computation. In this paper, we investigate how variational quantum algorithms could address this…
We design a variational quantum algorithm to solve multi-dimensional Poisson equations with mixed boundary conditions that are typically required in various fields of computational science. Employing an objective function that is formulated…
Quantum linear system algorithms (QLSAs) for gate-based quantum computing can provide exponential speedups for solving linear systems but face challenges when applied to finite element problems due to the growth of the condition number with…
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…
Variational quantum algorithms (VQAs) utilize a hybrid quantum-classical architecture to recast problems of high-dimensional linear algebra as ones of stochastic optimization. Despite the promise of leveraging near- to intermediate-term…
We present a hybrid classical-quantum algorithm to solve optimization problems in current quantum computers, whose basic idea is to assist variational quantum eigensolvers (VQE) with adiabatic change of the Hamiltonian. The rational for…
The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far either suffer from lack of accuracy and/or are limited to very small sizes of the…
Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers due to the extremely high computational cost. Quantum computers promise a solution,…
We present a novel variational quantum framework for linear partial differential equation (PDE) constrained optimization problems. Such problems arise in many scientific and engineering domains. For instance, in aerodynamics, the PDE…
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…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat…
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…
We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers. Specifically, we concatenate a variational quantum eigensolver (VQE) with a reduction in the…
Variational quantum algorithms have found success in the NISQ era owing to their hybrid quantum-classical approach which mitigate the problems of noise in quantum computers. In our study we introduce the dynamic ansatz in the Variational…
Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…
In this work, we present a case study in implementing a variational quantum algorithm for solving the Poisson equation, which is a commonly encountered partial differential equation in science and engineering. We highlight the practical…
Linear systems of equations can be found in various mathematical domains, as well as in the field of machine learning. By employing noisy intermediate-scale quantum devices, variational solvers promise to accelerate finding solutions for…
Solving problems related to planning and operations of large-scale power systems is challenging on classical computers due to their inherent nature as mixed-integer and nonlinear problems. Quantum computing provides new avenues to approach…
This paper presents a quantum algorithm for the solution of prototypical second-order linear elliptic partial differential equations discretized by $d$-linear finite elements on Cartesian grids of a bounded $d$-dimensional domain. An…