Related papers: Solving 1D Poisson problem with a Variational Quan…
In this article, we introduce an original hybrid quantum-classical algorithm based on a variational quantum algorithm for solving systems of differential equations. The algorithm relies on a spectral decomposition of the trial functions…
Variational quantum algorithms (VQAs) incorporate hybrid quantum-classical computation aimed at harnessing the power of noisy intermediate-scale quantum (NISQ) computers to solve challenging computational problems. In this thesis, three…
Linear system solvers are widely used in scientific computing, with the primary goal of solving linear system problems. Classical iterative algorithms typically rely on the conjugate gradient method. The rise of quantum computing has…
Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for…
Transition amplitudes and transition probabilities are relevant to many areas of physics simulation, including the calculation of response properties and correlation functions. These quantities can also be related to solving linear systems…
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…
We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for…
With the increasing popularity of quantum computing and in particular quantum annealing, there has been growing research to evaluate the meta-heuristic for various problems in linear algebra: from linear least squares to matrix and tensor…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
Variational Quantum Linear Solvers (VQLS) are a promising method for solving linear systems on near-term quantum devices. However, their performance is often limited by barren plateaus and inefficient parameter initialization, which…
With the advent of quantum computers, many quantum computing algorithms are being developed. Solving linear systems is one of the most fundamental problems in almost all science and engineering. The Harrow-Hassidim-Lloyd algorithm, a…
Although quantum computing holds promise for solving Combinatorial Optimization Problems (COPs), the limited qubit capacity of NISQ hardware makes large-scale instances intractable. Conventional methods attempt to bridge this gap through…
We solve Poisson's equation using new multigrid algorithms that converge rapidly. The novel feature of the 2D and 3D algorithms are the use of extra diagonal grids in the multigrid hierarchy for a much richer and effective communication…
In this paper, the author present reliable symbolic algorithms for solving a general bordered tridiagonal linear system. The first algorithm is based on the LU decomposition of the coefficient matrix and the computational cost of it is…
Variational quantum algorithms (VQAs) have the potential of utilizing near-term quantum machines to gain certain computational advantages over classical methods. Nevertheless, modern VQAs suffer from cumbersome computational overhead,…
The realization of quantum advantage with noisy-intermediate-scale quantum (NISQ) machines has become one of the major challenges in computational sciences. Maintaining coherence of a physical system with more than ten qubits is a critical…
Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore's law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world…
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…
This work studies the variational quantum eigensolver algorithm, designed to determine the ground state of a quantum mechanical system by combining classical and quantum hardware. Methods of reducing the number of required qubit…
Solving linear systems of equations is essential for many problems in science and technology, including problems in machine learning. Existing quantum algorithms have demonstrated the potential for large speedups, but the required quantum…