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Solving linear ordinary differential equations (ODE) is one of the most promising applications for quantum computers to demonstrate exponential advantages. The challenge of designing a quantum ODE algorithm is how to embed non-unitary…

Quantum Physics · Physics 2025-10-30 Zhong-Xia Shang , Naixu Guo , Dong An , Qi Zhao

Last years witnessed a remarkable interest in application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, even first proof-of-principle experimental realizations…

Quantum Physics · Physics 2013-05-30 Libor Veis , Jakub Višňák , Timo Fleig , Stefan Knecht , Trond Saue , Lucas Visscher , Jiří Pittner

Gradient-based local optimization has been shown to improve results of genetic programming (GP) for symbolic regression. Several state-of-the-art GP implementations use iterative nonlinear least squares (NLS) algorithms such as the…

Neural and Evolutionary Computing · Computer Science 2023-06-21 Gabriel Kronberger

Quantum chemistry has been viewed as one of the potential early applications of quantum computing. Two techniques have been proposed for electronic structure calculations: (i) the variational quantum eigensolver and (ii) the…

Quantum Physics · Physics 2021-04-19 Christina Daniel , Diksha Dhawan , Dominika Zgid , James K. Freericks

The conjugate gradient method (CG) is typically used with a preconditioner which improves efficiency and robustness of the method. Many preconditioners include parameters and a proper choice of a preconditioner and its parameters is often…

Numerical Analysis · Mathematics 2019-06-04 Alexandr Katrutsa , Mike Botchev , George Ovchinnikov , Ivan Oseledets

Classical optimization problems can be solved by adiabatically preparing the ground state of a quantum Hamiltonian that encodes the problem. The performance of this approach is determined by the smallest gap encountered during the…

Engineering the Hamiltonian of a quantum system is fundamental to the design of quantum systems. Automating Hamiltonian design through gradient-based optimization can dramatically accelerate this process. However, computing the gradients of…

With the aim of establishing a framework to efficiently perform the practical application of quantum chemistry simulation on near-term quantum devices, we envision a hybrid quantum--classical framework for leveraging problem decomposition…

The paper proposes a combination of the subdomain deflation method and local algebraic multigrid as a scalable distributed memory preconditioner that is able to solve large linear systems of equations. The implementation of the algorithm is…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-07-31 Denis Demidov , Riccardo Rossi

In this work, we propose an efficient adaptive multilevel preconditioned Jacobi-Davidson (PJD) method for eigenvalue problems with singularity. Our multilevel method utilizes a local smoothing strategy to solve the preconditioned…

Numerical Analysis · Mathematics 2026-05-14 Jianing Guo , Qigang Liang , Xuejun Xu

The variational quantum eigensolver is a hybrid algorithm composed of quantum state driving and classical parameter optimization, for finding the ground state of a given Hamiltonian. The natural gradient method is an optimization method…

Quantum Physics · Physics 2019-09-12 Naoki Yamamoto

Gaussian process hyperparameter optimization requires linear solves with, and log-determinants of, large kernel matrices. Iterative numerical techniques are becoming popular to scale to larger datasets, relying on the conjugate gradient…

Machine Learning · Computer Science 2022-06-22 Jonathan Wenger , Geoff Pleiss , Philipp Hennig , John P. Cunningham , Jacob R. Gardner

Our goal in this paper is to clarify the relationship between the block Lanczos and the block conjugate gradient (BCG) algorithms. Under the full rank assumption for the block vectors, we show the one-to-one correspondence between the…

Numerical Analysis · Mathematics 2025-02-25 Petr Tichý , Gérard Meurant , Dorota Šimonová

Molecular simulations are widely regarded as leading candidates to demonstrate quantum advantage--defined as the point at which quantum methods surpass classical approaches in either accuracy or scale. Yet the qubit counts and error rates…

Solving electronic structure problems is considered one of the most promising applications of quantum computing. However, due to limitations imposed by the coherence time of qubits in the Noisy Intermediate Scale Quantum (NISQ) era or the…

Quantum Physics · Physics 2025-03-20 Shuo Sun , Chandan Kumar , Kevin Shen , Elvira Shishenina , Christian B. Mendl

We present a hardware-efficient optimization scheme for quantum chemistry calculations, utilizing the Sampled Quantum Diagonalization (SQD) method. Our algorithm, optimized SQD (SQDOpt), combines the classical Davidson method technique with…

Quantum Physics · Physics 2025-03-05 Nora Bauer , Kübra Yeter-Aydeniz , George Siopsis

Quadratically Constrained Quadratic Programs (QCQPs) are an important class of optimization problems with diverse real-world applications. In this work, we propose a variational quantum algorithm for general QCQPs. By encoding the variables…

Quantum Physics · Physics 2023-09-20 Hongyi Zhou , Sirui Peng , Qian Li , Xiaoming Sun

The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks, which is an optimization algorithm for finding a local minimum of an objective function. The quantum versions of gradient…

Quantum Physics · Physics 2022-04-19 Jin-Min Liang , Shi-Jie Wei , Shao-Ming Fei

In recent years, topology optimization has been developed sufficiently and many researchers have concentrated on enhancing to computationally numerical algorithms for computational effectiveness of this method. Along with the development of…

Numerical Analysis · Mathematics 2023-01-19 Nam G. Luu , Thanh T. Banh