Related papers: Bridging quantum and classical computing for parti…
Variational quantum algorithms (VQAs) have established themselves as a central computational paradigm in the Noisy Intermediate-Scale Quantum (NISQ) era. By coupling parameterized quantum circuits (PQCs) with classical optimization, they…
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…
Reliable predictions of critical phenomena, such as weather, wildfires and epidemics often rely on models described by Partial Differential Equations (PDEs). However, simulations that capture the full range of spatio-temporal scales…
Quantum Phase Estimation is a crucial component of several front-running quantum algorithms. Improving the efficiency and accuracy of QPE is currently a very active field of research. In this work, we present a hybrid quantum-classical…
Quantum computers promise a great computational advantage over classical computers, yet currently available quantum devices have only a limited amount of qubits and a high level of noise, limiting the size of problems that can be solved…
We present a hybrid quantum-classical framework for solving general time-dependent parabolic partial differential equations (PDEs) using quantum variational circuits. Building on the QPINN approach, this method applies broadly to parabolic…
Neural networks (NNs) are often used as surrogates or emulators of partial differential equations (PDEs) that describe the dynamics of complex systems. A virtually negligible computational cost of such surrogates renders them an attractive…
Recent advances in quantum hardware motivate the development of algorithmic frameworks that integrate quantum sampling with classical inference. This work introduces a segmentation-based regression method tailored to quantum neural networks…
Fine-scale simulation of complex systems governed by multiscale partial differential equations (PDEs) is computationally expensive and various multiscale methods have been developed for addressing such problems. In addition, it is…
We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of…
Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…
This article presents a three-step framework for learning and solving partial differential equations (PDEs) using kernel methods. Given a training set consisting of pairs of noisy PDE solutions and source/boundary terms on a mesh, kernel…
Quantum computing hardware has grown sufficiently complex that it often can no longer be simulated by classical computers, but its computational power remains limited by errors. These errors corrupt the results of quantum algorithms, and it…
Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is…
Accurately solving high-dimensional partial differential equations (PDEs) remains a central challenge in computational mathematics. Traditional numerical methods, while effective in low-dimensional settings or on coarse grids, often…
In the recent years, numerous research advancements have extended the limit of classical simulation of quantum algorithms. Although, most of the state-of-the-art classical simulators are only limited to binary quantum systems, which…
Machine learning (ML) models have emerged as a promising approach for solving partial differential equations (PDEs) in science and engineering. Previous ML models typically cannot generalize outside the training data; for example, a trained…
The numerical solution of differential equations using neural networks has become a central topic in scientific computing, with Physics-Informed Neural Networks (PINNs) emerging as a powerful paradigm for both forward and inverse problems.…
We study a quantum-algorithmic framework for parameterizing partial differential equations (PDEs). For a broad class of problems in which the discretized parameter field admits a diagonal representation, block-encodings of diagonal…
Scientific and engineering problems often involve parametric partial differential equations (PDEs), such as uncertainty quantification, optimizations, and inverse problems. However, solving these PDEs repeatedly can be prohibitively…