# Diagrammatic Design and Study of Ans"atze for Quantum Machine Learning

arXiv: https://arxiv.org/abs/2011.11073 · HTML: https://mlsanity.com/paper/2011.11073/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Nov 2020.

## Built on by (most cited first, 5 of 5)

- [Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus](https://mlsanity.com/paper/2102.01828/) (2021)
- [Quantum Circuit Synthesis and Compilation Optimization: Overview and Prospects](https://mlsanity.com/paper/2407.00736/) (2024)
- [Diagrammatic Differentiation for Quantum Machine Learning](https://mlsanity.com/paper/2103.07960/) (2021)
- [Kindergarden quantum mechanics graduates (...or how I learned to stop gluing LEGO together and love the ZX-calculus)](https://mlsanity.com/paper/2102.10984/) (2021)
- [Differentiating and Integrating ZX Diagrams with Applications to Quantum Machine Learning](https://mlsanity.com/paper/2201.13250/) (2022)

## Abstract (arXiv)

Given the rising popularity of quantum machine learning (QML), it is important to develop techniques that effectively simplify commonly adopted families of parameterised quantum circuits (commonly known as ans"atze). This thesis pioneers the use of diagrammatic techniques to reason with QML ans"atze. We take commonly used QML ans"atze and convert them to diagrammatic form and give a full description of how these gates commute, making the circuits much easier to analyse and simplify. Furthermore, we leverage a combinatorial description of the interaction between CNOTs and phase gadgets to analyse a periodicity phenomenon in layered ans"atze and also to simplify a class of circuits commonly used in QML.