Related papers: Quantum multi-row iteration algorithm for linear s…
We present a quantum algorithm that analyzes time series data simulated by a quantum differential equation solver. The proposed algorithm is a quantum version of the dynamic mode decomposition algorithm used in diverse fields such as fluid…
Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from…
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…
Quantum computing holds significant promise for scientific computing due to its potential for polynomial to even exponential speedups over classical methods, which are often hindered by the curse of dimensionality. While neural networks…
We give a classical analogue to Kerenidis and Prakash's quantum recommendation system, previously believed to be one of the strongest candidates for provably exponential speedups in quantum machine learning. Our main result is an algorithm…
Variational quantum machine learning algorithms have been proposed as promising tools for time series prediction, with the potential to handle complex sequential data more effectively than classical approaches. However, their practical…
Harrow, Hassidim, and Lloyd showed that for a suitably specified $N \times N$ matrix $A$ and $N$-dimensional vector $\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of…
Quantum algorithms are known for presenting more efficient solutions to certain computational tasks than any corresponding classical algorithm. It has been thought that the origin of the power of quantum computation has its roots in…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
Due to recent technological advances, actual quantum devices are being constructed and used to perform computations. As a result, many classical problems are being restated so as to be solved on quantum computers. Some examples include…
Matrix scaling and matrix balancing are two basic linear-algebraic problems with a wide variety of applications, such as approximating the permanent, and pre-conditioning linear systems to make them more numerically stable. We study the…
Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…
Machines are possible to have some artificial intelligence like human beings owing to particular algorithms or software. Such machines could learn knowledge from what people taught them and do works according to the knowledge. In practical…
We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state $\vert x \rangle$ that is proportional to the solution of the system of linear equations $A…
Accurately predicting response properties of molecules such as the dynamic polarizability and hyperpolarizability using quantum mechanics has been a long-standing challenge with widespread applications in material and drug design. Classical…
Quantum computing enables the efficient resolution of complex problems, often outperforming classical methods across various applications. In 2009, Harrow, Hassidim and Lloyd proposed an algorithm for solving linear systems of equations,…
These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. So far, we have only discovered a few techniques which can produce speed up versus classical…
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,…