# Diagrammatic Differentiation for Quantum Machine Learning

@article{Toumi2021DiagrammaticDF, title={Diagrammatic Differentiation for Quantum Machine Learning}, author={Alexis Toumi and Richie Yeung and Giovanni de Felice}, journal={ArXiv}, year={2021}, volume={abs/2103.07960} }

We introduce diagrammatic differentiation for tensor calculus by generalising the dual number construction from rigs to monoidal categories. Applying this to ZX diagrams, we show how to calculate diagrammatically the gradient of a linear map with respect to a phase parameter. For diagrams of parametrised quantum circuits, we get the well-known parameter-shift rule at the basis of many variational quantum algorithms. We then extend our method to the automatic differentation of hybrid classical…

## 12 Citations

### How to make qubits speak

- EducationArXiv
- 2021

This is a story about making quantum computers speak, and doing so in a quantumnative, compositional and meaning-aware manner, and provides the reader with some indications of that broader pictorial landscape, including the authors' account on the notion of compositionality.

### Experimental Comparison of Ansätze for Quantum Natural Language Processing

- Computer Science
- 2022

A novel approach to overcome the out-of-vocabulary problem faced by contemporary QNLP models is proposed, and it is demonstrated that the proposed method outperforms naive approaches by a significant margin.

### Matrix differentiation with diagrammatic notation

- Computer Science
- 2022

A diagrammatic notation is proposed for matrix erentiation that enables formulas for matrix formulas to be derived more easily than the usual matrix (or index) notation.

### DisCoPy for the quantum computer scientist

- Computer Science
- 2022

This work reviews the recent developments of the library in this direction, making DisCoPy a toolbox for the quantum computer scientist.

### Diagrammatic Analysis for Parameterized Quantum Circuits

- Computer Science
- 2022

Extensions of the ZX-calculus especially suitable for parameterized quantum circuits, in particular for computing observable expectation values as functions of or for parameters, which are important algorithmic quantities in a variety of applications ranging from combinatorial optimization to quantum chemistry are described.

### Addition and Differentiation of ZX-Diagrams

- Computer ScienceFSCD
- 2022

This work introduces a general, inductive definition of the addition of ZX-diagrams, relying on the construction of controlled diagrams, and provides an inductive differentiation of Zx-displays, based on the isolation of variables.

### Differentiating and Integrating ZX Diagrams

- MathematicsArXiv
- 2022

ZX-calculus has proved to be a useful tool for quantum technology with a wide range of successful applications. Most of these applications are of an algebraic nature. However, other tasks that…

### Differentiating and Integrating ZX Diagrams with Applications to Quantum Machine Learning

- Computer Science
- 2022

The new analytic framework of ZX-calculus is illustrated by applying it in context of quantum machine learning for the analysis of barren plateaus by elevating ZX to an analytical perspective.

### Functorial Language Models (Work In Progress)

- Computer Science
- 2021

Functorial language models are introduced: a principled way to compute probability distributions over word sequences given a monoidal functor from grammar to meaning, which yields a method for training categorical compositional distributional (DisCoCat) models on raw text data.

### A Quantum Natural Language Processing Approach to Musical Intelligence

- Computer ScienceArXiv
- 2021

This chapter presents Quanthoven, the first proof-of-concept ever built, which demonstrates that it is possible to program a quantum computer to learn to classify music that conveys different meanings and illustrates how such a capability might be leveraged to develop a system to compose meaningful pieces of music.

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