API: Finite dimensional Quantum mechanics system

Finite dimensional Hilbert Space

Key data structure

The key data structure is the finite dimensional Hilbert space, which takes as an input the dimension of the Hilbert space. This is for a general system and not for any specific Hamiltonian.

• is defined

Need

Finite dimensional quantum mechanical systems are prevalent in lots of aspects of physics, including qubits in quantum information, and the Hilbert space of finite lattices. For example the tight binding chain.

Requirements

The following are requirements of the API:

• ability to easily define notation for basis vectors
• statements about the dimensions
• used in the definition of the qubit
• used in the definition of the tight binding chain
• easy conversion between bras and kets
• tensor products
• pure states

Corresponding File System

This file system exists, the link needs adding here.

Contributing to this API

This API is open to contributions from anyone. If you believe that the requirements outlined above need modification, feel free to comment here. If you make a PR which is related to this API, please link it to this issue.

Start by locating the existing finite-dimensional Hilbert space definition; the issue does not name a file, entry point, or test. Review the listed API requirements and determine how basis notation, dimension statements, qubits, tight-binding chains, bras and kets, tensor products, and pure states should be represented. Done means the required API elements are implemented and their use in the stated examples is demonstrated.