Related papers: Mitigating Barren Plateaus via Domain Decompositio…
Variational quantum algorithms are viewed as promising candidates for demonstrating quantum advantage on near-term devices. These approaches typically involve the training of parameterized quantum circuits through a classical optimization…
We propose an algorithm for variational quantum algorithms (VQAs) to optimize the structure of parameterized quantum circuits (PQCs) efficiently. The algorithm optimizes the PQC structure on-the-fly in VQA by sequentially replacing a…
Variational quantum algorithms (VQAs) promise efficient use of near-term quantum computers. However, training VQAs often requires an extensive amount of time and suffers from the barren plateau problem where the magnitude of the gradients…
Variational quantum algorithms (VQAs) are expected to establish valuable applications on near-term quantum computers. However, recent works have pointed out that the performance of VQAs greatly relies on the expressibility of the ansatzes…
In this paper, we present a new multiscale domain decomposition algorithm for computing solutions of static Eikonal equations. The new method is an iterative two-scale method that uses a parareal-like update scheme in combination with…
We propose new domain decomposition methods for systems of partial differential equations in two and three dimensions. The algorithms are derived with the help of the Smith factorization of the operator. This could also be validated by…
Variational quantum algorithms (VQAs) are a broad class of algorithms with many applications in science and industry. Applying a VQA to a problem involves optimizing a parameterized quantum circuit by maximizing or minimizing a cost…
Parameterized quantum circuits (PQCs) have emerged as a foundational element in the development and applications of quantum algorithms. However, when initialized with random parameter values, PQCs often exhibit barren plateaus (BP). These…
Variational quantum algorithms represent a powerful approach for solving optimization problems on noisy quantum computers, with a broad spectrum of potential applications ranging from chemistry to machine learning. However, their…
Variational Quantum Algorithms (VQAs) have received considerable attention due to their potential for achieving near-term quantum advantage. However, more work is needed to understand their scalability. One known scaling result for VQAs is…
We present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each…
In this paper, we propose a domain decomposition method for multiscale second order elliptic partial differential equations with highly varying coefficients. The method is based on a discontinuous Galerkin formulation. We present both a…
The simulation of complex systems, such as gas transport in large pipeline networks, often involves solving PDEs posed on intricate graph structures. Such problems require considerable computational and memory resources. The Random Batch…
We deal with the numerical solution of the time-dependent partial differential equations using the adaptive space-time discontinuous Galerkin (DG) method. The discretization leads to a nonlinear algebraic system at each time level, the size…
Variational quantum algorithms, which combine highly expressive parameterized quantum circuits (PQCs) and optimization techniques in machine learning, are one of the most promising applications of a near-term quantum computer. Despite their…
We develop a domain-decomposition model reduction method for linear steady-state convection-diffusion equations with random coefficients. Of particular interest to this effort are the diffusion equations with random diffusivities, and the…
Variational quantum algorithms are promising algorithms for achieving quantum advantage on near-term devices. The quantum hardware is used to implement a variational wave function and measure observables, whereas the classical computer is…
Parameterized quantum circuits (PQCs) have been widely used as a machine learning model to explore the potential of achieving quantum advantages for various tasks. However, training PQCs is notoriously challenging owing to the phenomenon of…
Variational Quantum Eigensolver (VQE) algorithms suffer from barren plateaus, where gradients vanish with system size and circuit depth. Although many mitigation strategies exist, their connection to convergence performance under different…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…