Computational Techniques

This guide provides a comprehensive look at how to access and select elements, subregions, and patterns within arrays and

This guide introduces the core containers provided by the Linear Algebra module, how to inspect them, and the day-to-day

- Operator transformations manipulate quantum expressions symbolically.

Linear Algebra is the fundamental package for numerical computing. At the core of the Linear Algebra package are the array and matrix objects. These encapsulate n-dimensional arrays of homogeneous data types, with many operations being performed in optimized compiled C++ code for performance. While Aleph is already documented at its core, Linear Algebra serves as the specialized linear algebra and array computation module, much like how NumPy extends Python's capabilities for scientific computing.

Introduction

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.

Array vs Matrix: Understanding the Difference

- Special transformations can be done on operator expressions comprised exclusively of spin 1/2 operators.

The tensors will eventually be replaced by the linear algebra module's array.