# Routed quantum circuits

**Authors:** Augustin Vanrietvelde, Hlér Kristjánsson, Jonathan Barrett  
**arXiv:** [2011.08120](https://arxiv.org/abs/2011.08120)  
**Date:** 2020-11-16  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2011.08120v1/

## Key points

- Authors: Augustin Vanrietvelde, Hlér Kristjánsson, Jonathan Barrett
- Discuss limitations of standard quantum circuit framework
- Propose extension with routed linear maps and circuits
- Allows for comprehensive diagrammatic representation
- Applicable to pure and mixed quantum theory
- Enables analysis of superposition of quantum channels and causal decompositions of unitaries
- Framework encompasses previous representations by Lorenz and Barrett
- Contributes to advancing understanding of complex quantum systems
- Valuable resource for researchers in quantum information processing

## Summary

In their paper titled "Routed Quantum Circuits," Augustin Vanrietvelde, Hlér Kristjánsson, and Jonathan Barrett discuss the limitations of the standard framework of quantum circuits in adequately describing complex quantum-theoretical structures. They propose an extension to the existing framework in the form of routed linear maps and circuits to address this issue. This extended framework allows for a more comprehensive and intuitive diagrammatic representation through circuit diagrams. It is applicable to both pure and mixed quantum theory, enabling effective analysis of scenarios such as superposition of quantum channels and causal decompositions of unitaries. The authors demonstrate that their proposed framework encompasses previous representations by Lorenz and Barrett, providing a solid semantic foundation for these diagrams. By expanding on existing concepts and introducing new tools for analysis, Vanrietvelde et al. contribute to advancing our understanding of complex quantum systems. Their paper serves as a valuable resource for researchers in the field of quantum information processing, offering insights into novel approaches for representing intricate structures beyond traditional circuit frameworks. The authors invite feedback on their work and encourage further exploration into the applications and implications of routed quantum circuits in theoretical physics.