# RTNI - A symbolic integrator for Haar-random tensor networks

## TL;DR

RTNI is a symbolic computation tool that calculates averages of tensor networks with Haar-random unitaries, aiding quantum information and holography research.

## Contribution

It introduces a novel computer algebra package implementing graphical Weingarten calculus for tensor network averages with symbolic dimensions.

## Key findings

- Successfully computes tensor network averages with Haar-random unitaries.
- Supports symbolic tensor dimensions and complex tensor contractions.
- Applied to entropy calculations in quantum information and holography models.

## Abstract

We provide a computer algebra package called Random Tensor Network Integrator (RTNI). It allows to compute averages of tensor networks containing multiple Haar-distributed random unitary matrices and deterministic symbolic tensors. Such tensor networks are represented as multigraphs, with vertices corresponding to tensors or random unitaries and edges corresponding to tensor contractions. Input and output spaces of random unitaries may be subdivided into arbitrary tensor factors, with dimensions treated symbolically. The algorithm implements the graphical Weingarten calculus and produces a weighted sum of tensor networks representing the average over the unitary group. We illustrate the use of this algorithmic tool on some examples from quantum information theory, including entropy calculations for random tensor network states as considered in toy models for holographic duality. Mathematica and Python implementations are supplied.