pyBoLaNO: A Python symbolic package for normal ordering involving bosonic ladder operators

TL;DR

pyBoLaNO is a Python package that automates the normal ordering of bosonic ladder operator polynomials, facilitating calculations in quantum optics and open quantum systems with enhanced efficiency and versatility.

Contribution

This work introduces pyBoLaNO, a novel Python package that automates normal ordering of bosonic operators, including commutators and expectation values, with support for multipartite systems and multiprocessing.

Findings

Efficient normal ordering of bosonic polynomials demonstrated.

Supports calculation of expectation values in Lindblad dynamics.

Open-source implementation with performance discussion.

Abstract

We present pyBoLaNO, a Python symbolic package based on SymPy to quickly normal-order (Wick-order) any polynomial in bosonic ladder operators. By extension, this package offers the normal ordering of commutators of any two polynomials in bosonic ladder operators and the evaluation of the normal-ordered expectation value evolution in the Lindblad master equation framework for open quantum systems. The package also supports multipartite descriptions and multiprocessing. We describe the package's workflow, show examples of use, and discuss its computational performance. All codes and examples are available on our GitHub repository.