# Quantum Walk and Quantum Billiards. Towards a better understanding of Quantum Chaos

## TL;DR

This paper introduces a new approximation method for simulating quantum billiards, leveraging tensor products of 1-D quantum walks, to better understand quantum chaos in both chaotic and non-chaotic systems.

## Contribution

It presents a novel approximation approach for quantum billiards based on tensor products of 1-D quantum walks, enhancing the analysis of quantum chaos.

## Key findings

- Chaotic and non-chaotic billiards are effectively tested.
- The new approximation provides insights into quantum chaos.
- Supports better simulation of quantum billiard systems.

## Abstract

Quantum billiards have been simulated so far in many ways, but in this work a new aproximation is considerated. This study is based on the quantum billiard already obtained by others authors via a tensor product of two 1-D quantum walks . Chaotic and non chaotic billiards are tested.