Quantum simulation

Floquet models, or more generally quantum circuit models, are two common systems in the study of quantum many body physics. They offer a minimal environment for the study of dynamics and chaos, while also being closely related quantum information and computing contexts. In this tutorial we will discuss both classes of models and how to work with them numerically.

In this tutorial we use the quantum toolkit, specifically the operator framework and the free fermion features, to study the dynamics and eigenstates of a free fermion system. For a comprehensive introduction to free fermion systems and their representation, see the concept Non-interacting fermions.

At a glance

This section covers numerical methods for simulating quantum systems, including exact diagonalization, time evolution, and tensor network techniques. We provide code examples that can be run in the Workshop to help you understand how to implement these methods and apply them to various quantum models.

Evolving quantum states is a common routine in numerical methods. There are many ways to do this, the most common and accessible being full exact diagonalization and evolving an initial state using knowledge of the full spectrum of a Hamiltonian $H$,

In the Heisenberg picture of quantum mechanics, operators evolve in time while states remain fixed.

This section focuses on the time evolution of quantum systems, including both unitary and non-unitary dynamics. We explore how to simulate the time evolution of quantum states and operators, and how to analyze the resulting dynamics. Each tutorial includes code examples that can be run in the Workshop to reproduce results and gain hands-on experience with these concepts.