Related papers: Resource-efficient quantum algorithm for linear sy…
Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution exponentially faster than classical algorithms in terms of…
Quantum computing has the potential to speed up some optimization methods. One can use quantum computers to solve linear systems via Quantum Linear System Algorithms (QLSAs). QLSAs can be used as a subroutine for algorithms that require…
We propose a natural application of Quantum Linear Systems Problem (QLSP) solvers such as the HHL algorithm to efficiently prepare highly excited interior eigenstates of physical Hamiltonians in a variational and targeted manner. This is…
Previously proposed quantum algorithms for solving linear systems of equations cannot be implemented in the near term due to the required circuit depth. Here, we propose a hybrid quantum-classical algorithm, called Variational Quantum…
Variational Quantum Algorithms (VQAs) have emerged as promising methods for tackling complex problems on near-term quantum devices. Among these algorithms, the Variational Quantum Linear Solver (VQLS) addresses linear systems of the form…
Finding solutions to systems of linear equations is a common prob\-lem in many areas of science and engineering, with much potential for a speedup on quantum devices. While the Harrow-Hassidim-Lloyd (HHL) quantum algorithm yields up to an…
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…
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…
Solving linear systems of equations plays a fundamental role in numerous computational problems from different fields of science. The widespread use of numerical methods to solve these systems motivates investigating the feasibility of…
Solving systems of linear equations is a fundamental problem, but it can be computationally intensive for classical algorithms in high dimensions. Existing quantum algorithms can achieve exponential speedups for the quantum linear system…
Different hybrid quantum-classical algorithms have recently been developed as a near-term way to solve linear systems of equations on quantum devices. However, the focus has so far been mostly on the methods, rather than the problems that…
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…
State-of-the-art noisy intermediate-scale quantum devices (NISQ), although imperfect, enable computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, present quantum computations are…
Gaussian processes are widely known for their ability to provide probabilistic predictions in supervised machine learning models. Their non-parametric nature and flexibility make them particularly effective for regression tasks. However,…
Despite the successful enhancement to the Harrow-Hassidim-Lloyd algorithm by Childs et al., who introduced the Fourier approach leveraging linear combinations of unitary operators, our research has identified non-trivial redundancies within…
Variational quantum algorithms (VQAs) are promising hybrid quantum-classical methods designed to leverage the computational advantages of quantum computing while mitigating the limitations of current noisy intermediate-scale quantum (NISQ)…
The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution of a linear system provides an exponential speed-up over its classical counterpart. The problem of solving a system of linear equations has a wide scope of…
The prosperous development of both hardware and algorithms for quantum computing (QC) potentially prompts a paradigm shift in scientific computing in various fields. As an increasingly active topic in QC, the variational quantum algorithm…
This paper explores the use of quantum computing, specifically the use of HHL and VQLS algorithms, to solve optimal power flow problem in electrical grids. We investigate the effectiveness of these quantum algorithms in comparison to…
Quantum computing, a prominent non-Von Neumann paradigm beyond Moore's law, can offer superpolynomial speedups for certain problems. Yet its advantages in efficiency for tasks like machine learning remain under investigation, and quantum…