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Performing analog computations with metastructures is an emerging wave-based paradigm for solving mathematical problems. For such devices, one major challenge is their reconfigurability, especially without the need for a priori mathematical…
This paper presents a new approach which uses the tools within Artificial Intelligence (AI) software libraries as an alternative way of solving partial differential equations (PDEs) that have been discretised using standard numerical…
The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations. The algorithms are…
A linear-algebraic theory called 'multiple Arnoldi method' is presented and realizes large-scale (order-N) electronic structure calculation with generalized eigen-value equations. A set of linear equations, in the form of (zS-H) x = b, are…
The Variational Quantum Linear Solver (VQLS), a hybrid quantum-classical algorithm for solving linear systems, faces a practical scalability bottleneck: the Linear Combination of Unitaries (LCU) decomposition requires O(L^2) circuit…
Many optimization problems require hyperparameters, i.e., parameters that must be pre-specified in advance, such as regularization parameters and parametric regularizers in variational regularization methods for inverse problems, and…
Quantum computing is entering a transformative phase with the emergence of logical quantum processors, which hold the potential to tackle complex problems beyond classical capabilities. While significant progress has been made, applying…
We present a Newton-Krylov solver for a viscous-plastic sea-ice model. This constitutive relation is commonly used in climate models to describe the material properties of sea ice. Due to the strong nonlinearity introduced by the material…
The demand for substantial increases in the spatial resolution of global weather- and climate- prediction models makes it necessary to use numerically efficient and highly scalable algorithms to solve the equations of large scale…
Quantum systems have historically been formidable to simulate using classical computational methods, particularly as the system size grows. In recent years, advancements in quantum computing technology have offered new opportunities for…
The variational quantum eigensolver (VQE) is a hybrid algorithm that has the potential to provide a quantum advantage in practical chemistry problems that are currently intractable on classical computers. VQE trains parameterized quantum…
We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers. Specifically, we concatenate a variational quantum eigensolver (VQE) with a reduction in the…
The Variational Quantum Eigensolver (VQE) is a promising algorithm for quantum computing applications in chemistry and materials science, particularly in addressing the limitations of classical methods for complex systems. This study…
Neutronic calculations for reactors are a daunting task when using Monte Carlo (MC) methods. As high-performance computing has advanced, the simulation of a reactor is nowadays more readily done, but design and optimization with multiple…
In many scientific applications the solution of non-linear differential equations are obtained through the set-up and solution of a number of successive eigenproblems. These eigenproblems can be regarded as a sequence whenever the solution…
In the midst of the neural network's success in solving partial differential equations, tackling eigenvalue problems using neural networks remains a challenging task. However, the Physics Constrained-General Inverse Power Method Neural…
This paper presents a strategy for the computation of structures with repeated patterns based on domain decomposition and block Krylov solvers. It can be seen as a special variant of the FETI method. We propose using the presence of…
This research introduce our work on developing Krylov subspace and AMG solvers on NVIDIA GPUs. As SpMV is a crucial part for these iterative methods, SpMV algorithms for single GPU and multiple GPUs are implemented. A HEC matrix format and…
Many problems are governed by differential equations (DEs). Artificial intelligence (AI) is a new path for solving DEs. However, data is very scarce and existing AI solvers struggle with approximation of high frequency components (AHFC). We…
We introduce a multireference selected quantum Krylov (MRSQK) algorithm suitable for quantum simulation of many-body problems. MRSQK is a low-cost alternative to the quantum phase estimation algorithm that generates a target state as a…