Hamiltonian systems

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 $H$,

Operators are a central tool for expressing and solving quantum many-body physics problems in Aleph. They underpin Aleph's ability to mix symbolic computation with numerical methods. Operators simplify the expression of quantum objects while avoiding costly memory allocations. This guide reviews the general operator framework.

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.