Quantum Simulation

| Type classification: this resource is a course.

|

| Completion status: this resource is considered to be complete.

|

The first part of the course will discuss various state of the art methods for the numerical description of many-body quantum systems. In particular, I will explain successful applications and inherent limitations due to the exponential complexity of the many-body problem.

In the second part of the course, I will show how using highly controllable quantum system such as ultracold atoms will provide a way to overcome the limitations of classical simulation methods. I will discuss several theoretical and experimental achievements and outline the road for future developments.

## Classical simulation of quantum systems

[edit | edit source]

### Exact diagonalization

[edit | edit source]

### Quantum Monte-Carlo

[edit | edit source]

### Density-Matrix Renormalization Group

[edit | edit source]

## Quantum simulation with ultracold atoms

[edit | edit source]

### Analog quantum simulation

[edit | edit source]

### Digital quantum simulation

[edit | edit source]