**Numerical analysis on quantum computers (VO, 2h, 3ECTS) **

Markus Faustmann
Michael Feischl
We explain the basics of quantum computers (what is required in order to play numerical analysis) and analyze a number of algorithms:

- Grover's algorithm (search in unsorted vectors in $\mathcal{O}(\sqrt{N})$ )
- Shor's algorithm (factorization in polynomial time)
- Solving sparse linear systems (with exponential speed-up over classical algorithms)
- Differential equations on quantum computers

Weekly lectures: Tue 9-10:30 (Seminarraum 3B, grün), Thu 10-11 (Seminarraum 3A, grün)

### lecture notes:

- Slides from first lecture
- Part 1: Basics of quantum computers
- Part 2: Classical quantum algorithms (last update 23.5.2023)
- Part 3: Solving linear systems (last update 9.6.2023)
- Part 4: Solving linear differential equations (last update 22.6.2023)

### examples in IBM Quantum Composer:

- Solving a 2x2 system (see lecture notes)
- Grover Algorithm with $F(x) = x_0x_1x_2x_3$ (requires free account)
- Deutsch-Josza Algorithm with $F(x) = x_0\oplus x_1x_2$ (requires free account)
- Quantum Teleportation

### other material: