Related papers: Quantum Kernel Methods for Solving Differential Eq…
Quantum algorithms for both differential equation solving and for machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in…
Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the…
The kernel matrix used in kernel methods encodes all the information required for solving complex nonlinear problems defined on data representations in the input space using simple, but implicitly defined, solutions. Spectral analysis on…
We develop an approach for building quantum models based on the exponentially growing orthonormal basis of Hartley kernel functions. First, we design a differentiable Hartley feature map parametrized by real-valued argument that enables…
Kernel methods are used extensively in classical machine learning, especially in the field of pattern analysis. In this paper, we propose a kernel-based quantum machine learning algorithm that can be implemented on a near-term, intermediate…
Quantum Machine Learning (QML) is considered to be one of the most promising applications of near term quantum devices. However, the optimization of quantum machine learning models presents numerous challenges arising from the imperfections…
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…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One example of such a hybrid quantum-classical approach is the variational quantum eigensolver (VQE) built to…
Quantum machine learning (QML) is the use of quantum computing for the computation of machine learning algorithms. With the prevalence and importance of classical data, a hybrid quantum-classical approach to QML is called for. Parameterized…
The functional characterization of different neuronal types has been a longstanding and crucial challenge. With the advent of physical quantum computers, it has become possible to apply quantum machine learning algorithms to translate…
Kernel methods are an important class of techniques in machine learning. To be effective, good feature maps are crucial for mapping non-linearly separable input data into a higher dimensional (feature) space, thus allowing the data to be…
Quantum machine learning techniques have been proposed as a way to potentially enhance performance in machine learning applications. In this paper, we introduce two new quantum methods for neural networks. The first one is a quantum…
Recent advancements in quantum computing (QC) and machine learning (ML) have garnered significant attention, leading to substantial efforts toward the development of quantum machine learning (QML) algorithms to address a variety of complex…
Physics-informed machine learning (PIML) has emerged as a promising alternative to conventional numerical methods for solving partial differential equations (PDEs). PIML models are increasingly built via deep neural networks (NNs) whose…
We propose a quantum machine learning framework for approximating solutions to high-dimensional parabolic partial differential equations (PDEs) that can be reformulated as backward stochastic differential equations (BSDEs). In contrast to…
We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an $N\times N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\textbf{\emph{b}}$, and an initial vector $\textbf{\emph{x}}(0)$,…
Differential equations (DEs) serve as the cornerstone for a wide range of scientific endeavors, their solutions weaving through the core of diverse fields such as structural engineering, fluid dynamics, and financial modeling. DEs are…
Quantum computing opens exciting opportunities for kernel-based machine learning methods, which have broad applications in data analysis. Recent works show that quantum computers can efficiently construct a model of a classifier by…
Variational quantum eigensolvers (VQEs) combine classical optimization with efficient cost function evaluations on quantum computers. We propose a new approach to VQEs using the principles of measurement-based quantum computation. This…