# Charged String Tensor Networks

## TL;DR

This paper explores a new class of tensor networks called the JLW-model, which incorporates charge excitations and offers a novel graphical reasoning framework for quantum information and topological quantum computing.

## Contribution

It introduces and analyzes the JLW-model of tensor networks, highlighting its charge-based structure and potential for alternative quantum reasoning methods.

## Key findings

- JLW-model incorporates charge excitations in tensor networks
- Graphical manipulations encode complex quantum information transformations
- Open problems in the model's application to quantum protocols

## Abstract

Tensor network methods provide an intuitive graphical language to describe quantum states, channels, open quantum systems and a class of numerical approximation methods that efficiently simulate certain many-body states in one spatial dimension. There are two fundamental types of tensor networks in wide use today. The most common is similar to quantum circuits. The second is the braided class of tensor networks, used in topological quantum computing. Recently a third class of tensor networks was discovered by Jaffe, Liu and Wozniakowski---the JLW-model---notably, the wires carry charge excitations. The rules in which network components can be moved, merged and manipulated in a graphical form of reasoning take an elegant form. For instance the relative charge locations on wires carries precise meaning and changing the ordering modifies a connected network specifically by a complex number. The type of isotopy discovered in the topological JLW-model provides an alternative means to reason about quantum information, computation and protocols. Here we recall the tensor-network building blocks used in a controlled-NOT gate. Some open problems related to the JLW-model are given.