Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

110
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
110
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

88
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
88
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

540
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
540
Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

14.1K
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
14.1K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

120
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
120
Virtual Work for a System of Connected Rigid Bodies01:06

Virtual Work for a System of Connected Rigid Bodies

435
Virtual work is a powerful method used to solve problems involving several connected rigid bodies. When the system is in equilibrium, virtual work is zero. This allows the calculation of the resulting forces when a system undergoes a virtual displacement. When attempting to analyze such a system, first, use a free-body diagram, where an independent coordinate represents the configuration of the links, and mark its deflected position resulting from the positive virtual displacement.
Next,...
435

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Effect of Health Literacy on use of a Virtual Coach to Promote Home Blood Pressure Monitoring.

Journal of clinical hypertension (Greenwich, Conn.)·2026
Same author

Recommendations for Empiric Antibiotic Therapy in Hidradenitis Suppurativa.

Cutis·2025
Same author

Augmenting Engagement in Decentralized Clinical Trials for Atrial Fibrillation: Development and Implementation of a Programmatic Architecture.

JMIR cardio·2025
Same author

Quantum Physics-Informed Neural Networks.

Entropy (Basel, Switzerland)·2024
Same author

FDG Avid Intracholecystic Papillary Neoplasm Mimicking Hepatic Metastasis in a Patient with Head-and-neck Cancer.

Indian journal of nuclear medicine : IJNM : the official journal of the Society of Nuclear Medicine, India·2024
Same author

Impacts of Rumen Degradable or Undegradable Protein Supplementation on Supplement Intake and Performance of Yearling Heifers and Cows Grazing Dryland Pastures.

Animals : an open access journal from MDPI·2022
Same journal

Research on a Regional Availability Evaluation Model for Road-Area High-Entropy Energy Based on Synergy Factors.

Entropy (Basel, Switzerland)·2026
Same journal

Atmospheric Turbulence Channel Modeling and Performance Analysis of a CO-ZP-OFDM Coherent Optical Communication System for UAV Air-to-Ground Scenarios.

Entropy (Basel, Switzerland)·2026
Same journal

Information Geometry and Asymptotic Theory for SMML Estimators.

Entropy (Basel, Switzerland)·2026
Same journal

Correlation Entropy and Power-Law Kinetics.

Entropy (Basel, Switzerland)·2026
Same journal

Research on the Contagion of Systemic Financial Risk Under the Impact of Climate Risks-From the Perspective of Complex Networks and Machine Learning.

Entropy (Basel, Switzerland)·2026
Same journal

The Statistical-Mechanical Meaning of the Wave Function of Quantum Mechanics.

Entropy (Basel, Switzerland)·2026
See all related articles

Related Experiment Video

Updated: Jul 30, 2025

Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

3.5K

A Variational Quantum Linear Solver Application to Discrete Finite-Element Methods.

Corey Jason Trahan1, Mark Loveland1, Noah Davis2

  • 1Information and Technology Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS 39180, USA.

Entropy (Basel, Switzerland)
|May 16, 2023
PubMed
Summary
This summary is machine-generated.

This study explores the variational quantum linear solver (VQLS) for solving partial differential equations. The quantum approach shows promise for efficiently handling large-scale problems on near-term quantum computers.

Keywords:
Poisson equationfinite-element methodsheat equationquantum algorithmsquantum computingquantum variational algorithm

More Related Videos

Author Spotlight: Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques
07:16

Author Spotlight: Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques

Published on: October 20, 2023

1.4K
Author Spotlight: Streamlining Visual Dynamics to Simplify Molecular Dynamics Simulations Using Gromacs
05:00

Author Spotlight: Streamlining Visual Dynamics to Simplify Molecular Dynamics Simulations Using Gromacs

Published on: August 9, 2024

1.4K

Related Experiment Videos

Last Updated: Jul 30, 2025

Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

3.5K
Author Spotlight: Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques
07:16

Author Spotlight: Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques

Published on: October 20, 2023

1.4K
Author Spotlight: Streamlining Visual Dynamics to Simplify Molecular Dynamics Simulations Using Gromacs
05:00

Author Spotlight: Streamlining Visual Dynamics to Simplify Molecular Dynamics Simulations Using Gromacs

Published on: August 9, 2024

1.4K

Area of Science:

  • Computational Science
  • Quantum Computing
  • Numerical Analysis

Background:

  • Finite-element methods are standard for solving partial differential equations but face scalability challenges with large linear systems.
  • Classical solvers struggle with the computational demands of large-scale, multi-scale applications, limiting practical use even on supercomputers.
  • Investigating quantum algorithms for linear system solutions is crucial for advancing computational capabilities.

Purpose of the Study:

  • To evaluate the potential of the variational quantum linear solver (VQLS) for solving discrete partial differential equations.
  • To assess the scalability and feasibility of VQLS on noisy intermediate-scale quantum (NISQ) computers.
  • To demonstrate the application of VQLS to benchmark equations like the Poisson, heat, and wave equations.

Main Methods:

  • The study utilizes the hybrid variational quantum linear solver (VQLS) algorithm.
  • The VQLS method is applied to discrete formulations of the steady Poisson equation and time-dependent heat and wave equations.
  • Implementation considers shallow quantum circuits suitable for NISQ devices.

Main Results:

  • The VQLS method demonstrates polylogarithmic scaling with respect to the linear system size.
  • The approach is compatible with shallow quantum circuits, making it suitable for current NISQ hardware.
  • Successful application of VQLS to solve the Poisson, heat, and wave equations was achieved.

Conclusions:

  • The variational quantum linear solver (VQLS) offers a promising quantum advantage for solving large-scale linear systems arising from partial differential equations.
  • VQLS presents a viable approach for near-term quantum computers, addressing limitations of classical methods.
  • This work validates VQLS for key differential equations, paving the way for quantum-enhanced scientific computing.