Numerical methods for quantum computation

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Applied Mathematics

Synopsis:

The course is devoted to numerical solution of boundary-value problems and intial-boundary-value problems for ordinary and partial differential equations. It explains finite-difference, finite-element and finite-volume methods for elliptic, parabolic and hyperbolic partial differential equations. Students are introduced to the recent advances in methods solving the mentioned problems.

Requirements:

Syllabus of lectures:

1. Motivation examples and classification of problems.

2. Basics of numerical algorithms - validation, verification, parametar dependence, convergence.

3. Solution of algebraic systems of equations.

4. Solution of ordinary differential equations.

5. Solution of differential algebraic equations.

6. Solution of stationary partial differential equations.

7. Solution of evolution partial differential equations.

8. Finite-difference method.

9. Finite-volume method.

10. Finite-element method.

11. Applications in quantum computing: multibody systems.

12. Applications in quantum computing: Navier-Stokes equations.

13. Applications in quantum computing: Maxwell equations.

Syllabus of tutorials:

1. Motivation examples and classification of problems - exercises with models

2. Basics of numerical algorithms - validation, verification, parametar dependence, convergence - exercises with models

3. Solution of algebraic systems of equations - implementation and comparison with existing functions

4. Solution of ordinary differential equations - examples

5. Solution of differential algebraic equations - examples

6. Solution of stationary partial differential equations - examples

7. Solution of evolution partial differential equations - examples

8. Finite-difference method - implementation

9. Finite-volume method - implementation

10. Finite-element method - problems from continuum mechanics

11. Applications in quantum computing: multibody systems

12. Applications in quantum computing: Navier-Stokes equations - implementation using templates

13. Applications in quantum computing: Maxwell equations

Study Objective:

The course is devoted to numerical solution of boundary-value problems and intial-boundary-value problems for ordinary and partial differential equations. It explains finite-difference, finite-element and finite-volume methods for elliptic, parabolic and hyperbolic partial differential equations. Students are introduced to the recent advances in methods solving the mentioned problems.

Study materials:

1. Quarteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics, Texts in Applied Mathematics

Springer 2007, ISBN 978-3-540-34658-6

2. LeVeque, R. J.: Numerical methods for conservation laws

Birkhäuser 1992, ISBN 978-3-7643-2723-1

3. Stejskal, V., Valasek, M.: Kinematics and Dynamics of Machinery

Marcel Dekker 1996, ISBN 0-8247-9731-0

4. Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems

Springer 1996, ISBN 978-3-540-60452-5

Note:

This course is presented in English.

Further information:

https://courses.fit.cvut.cz/QNIE-NMK

No time-table has been prepared for this course

The course is a part of the following study plans: