TensorKit.jl: A Julia package for large-scale tensor computations, with a hint of category theory

TL;DR

TensorKit.jl is a Julia package that enables efficient large-scale tensor computations with internal symmetries, leveraging category theory concepts for flexible and extensible tensor operations.

Contribution

The paper introduces TensorKit.jl, a novel Julia package that supports advanced tensor symmetries and extensibility, enhancing computational efficiency and flexibility.

Findings

Supports abelian, non-abelian, and anyonic symmetries

Demonstrates high performance and flexibility in tensor computations

Applicable to various practical tensor problems

Abstract

TensorKit.jl is a Julia-based software package for tensor computations, especially focusing on tensors with internal symmetries. This paper introduces the design philosophy, core functionalities, and distinctive features, including how to handle abelian, non-abelian, and anyonic symmetries through the ``TensorMap'' type. We highlight the software's flexibility, performance, and its capability to extend to new tensor types and symmetries, illustrating its practical applications through select case studies.