Related papers: High-order quantum algorithm for solving linear di…
We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms…
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,…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…
Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several…
As industrial models and designs grow increasingly complex, the demand for optimal control of large-scale dynamical systems has significantly increased. However, traditional methods for optimal control incur significant overhead as problem…
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…
Quantum computing is an advancing area of research in which computer hardware and algorithms are developed to take advantage of quantum mechanical phenomena. In recent studies, quantum algorithms have shown promise in solving linear systems…
Digital quantum computers provide a computational framework for solving the Schr\"{o}dinger equation for a variety of many-particle systems. Quantum computing algorithms for the quantum simulation of these systems have recently witnessed…
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…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical…
The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
We describe a quantum algorithm that generalizes the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We develop a state preparation routine that can initialize…
Efficiently solving large-scale sparse linear systems poses a significant challenge in computational science, especially in fields such as physics, engineering, machine learning, and finance. Traditional classical algorithms face…