Related papers: Resource-efficient quantum algorithm for linear sy…
With the rapid development of quantum computers, quantum algorithms have been studied extensively. However, quantum algorithms tackling statistical problems are still lacking. In this paper, we propose a novel non-oracular quantum adaptive…
Quantum linear-system algorithms (QLSAs) have rigorous worst-case complexity guarantees, but their runtimes are often chosen from spectral information assumed in advance. What is largely lacking is an a posteriori progress flag: most QLSA…
Quantum computing, leveraging principles of quantum mechanics, represents a transformative approach in computational methodologies, offering significant enhancements over traditional classical systems. This study tackles the complex and…
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…
A promising area of applications for quantum computing is in linear algebra problems. In this work, we introduce two new quantum t-SVD (tensor-SVD) algorithms. The first algorithm is largely based on previous work that proposed a quantum…
This paper presents a numerical method based on the variational quantum algorithm to solve potential and Stokes flow problems. In this method, the governing equations for potential and Stokes flows can be respectively written in the form of…
Simulation of realistic classical mechanical systems is of great importance to many areas of engineering such as robotics, dynamics of rotating machinery and control theory. In this work, we develop quantum algorithms to estimate quantities…
The Vlasov-Maxwell system of equations, which describes classical plasma physics, is extremely challenging to solve, even by numerical simulation on powerful computers. By linearizing and assuming a Maxwellian background distribution…
We present a systematic pathway for solving differential equations within the quantum linear systems framework by combining block encoding with Quantum Singular Value Transformation (QSVT). The approach is demonstrated on a complex…
This work presents a quantum algorithm for solving linear systems of equations of the form $\mathbf{A}{\frac{\mathbf{\partial f}}{\mathbf{\partial x}}} = \mathbf{B}\mathbf{f}$, based on the Quantum Singular Value Transformation (QSVT). The…
Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…
Quantization can be used to form new vectors/matrices with shared values close to the original. In recent years, the popularity of scalar quantization for value-sharing applications has been soaring as it has been found huge utilities in…
The development of quantum processors capable of handling practical fluid flow problems represents a distant yet promising frontier. Recent strides in quantum algorithms, particularly linear solvers, have illuminated the path toward quantum…
Solving systems of linear equations is a key subroutine in many quantum algorithms. In the last 15 years, many quantum linear solvers (QLS) have been developed, competing to achieve the best asymptotic worst-case complexity. Most QLS assume…
Solving optimization problems is a key task for which quantum computers could possibly provide a speedup over the best known classical algorithms. Particular classes of optimization problems including semi-definite programming (SDP) and…
Great progress has been made in quantum computing in recent years, providing opportunities to overcome computation resource poverty in many scientific computations like computational fluid dynamics (CFD). In this work, efforts are made to…
HHL algorithm \cite{harrow} to solve linear system is a powerful and efficient quantum technique to deal with many matrix operations (such as matrix multiplication, powers and inversion). It inspires many applications in quantum machine…
A novel parallel hybrid quantum-classical algorithm for the solution of the quantum-chemical ground-state energy problem on gate-based quantum computers is presented. This approach is based on the reduced density-matrix functional theory…
We develop a novel approach for efficiently applying variational quantum linear solver (VQLS) in context of structured sparse matrices. Such matrices frequently arise during numerical solution of partial differential equations which are…
For quantum computing (QC) to emerge as a practically indispensable computational tool, there is a need for quantum protocols with an end-to-end practical applications -- in this instance, fluid dynamics. We debut here a high performance…