# Geometrical perspective on quantum states and quantum computation

**Authors:** Zeqian Chen  
**arXiv:** [1311.4939](https://arxiv.org/abs/1311.4939)  
**Date:** 2013-11-20  
**Summary page:** https://www.summarizepaper.com/en/paper/1311.4939v1/

## Abstract

We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge transformations on the connections play a role of unitary quantum operations. Thereby, a geometrical model for quantum computation is presented, which is equivalent to the quantum circuit model. This result shows a geometric way of realizing quantum computing and as such, provides an alternative proposal of building a quantum computer.