Diagrammatic differentiation for quantum machine learning
We introduce diagrammatic differentiation for tensor calculus by generalising the dual
number construction from rigs to monoidal categories. Applying this to ZX diagrams, we …
number construction from rigs to monoidal categories. Applying this to ZX diagrams, we …
[图书][B] Introducing string diagrams: the art of category theory
R Hinze, D Marsden - 2023 - books.google.com
String diagrams are powerful graphical methods for reasoning in elementary category
theory. Written in an informal expository style, this book provides a self-contained …
theory. Written in an informal expository style, this book provides a self-contained …
An introduction to string diagrams for computer scientists
R Piedeleu, F Zanasi - arXiv preprint arXiv:2305.08768, 2023 - arxiv.org
This document is an elementary introduction to string diagrams. It takes a computer science
perspective: rather than using category theory as a starting point, we build on intuitions from …
perspective: rather than using category theory as a starting point, we build on intuitions from …
Category theory for quantum natural language processing
A Toumi - arXiv preprint arXiv:2212.06615, 2022 - arxiv.org
This thesis introduces quantum natural language processing (QNLP) models based on a
simple yet powerful analogy between computational linguistics and quantum mechanics …
simple yet powerful analogy between computational linguistics and quantum mechanics …
String-net models for pivotal bicategories
J Fuchs, C Schweigert, Y Yang - arXiv preprint arXiv:2302.01468, 2023 - arxiv.org
We develop a string-net construction of a modular functor whose algebraic input is a pivotal
bicategory; this extends the standard construction based on a spherical fusion category. An …
bicategory; this extends the standard construction based on a spherical fusion category. An …
Open diagrams via coend calculus
M Román - arXiv preprint arXiv:2004.04526, 2020 - arxiv.org
Morphisms in a monoidal category are usually interpreted as processes, and graphically
depicted as square boxes. In practice, we are faced with the problem of interpreting what …
depicted as square boxes. In practice, we are faced with the problem of interpreting what …
Pictures of processes: automated graph rewriting for monoidal categories and applications to quantum computing
A Kissinger - arXiv preprint arXiv:1203.0202, 2012 - arxiv.org
This work is about diagrammatic languages, how they can be represented, and what they in
turn can be used to represent. More specifically, it focuses on representations and …
turn can be used to represent. More specifically, it focuses on representations and …
Rewriting for monoidal closed categories
M Alvarez-Picallo, D Ghica, D Sprunger… - … Conference on Formal …, 2022 - drops.dagstuhl.de
This paper develops a formal string diagram language for monoidal closed categories.
Previous work has shown that string diagrams for freely generated symmetric monoidal …
Previous work has shown that string diagrams for freely generated symmetric monoidal …
Resource modalities in tensor logic
PA Melliès, N Tabareau - Annals of Pure and Applied Logic, 2010 - Elsevier
The description of resources in game semantics has never achieved the simplicity and
precision of linear logic, because of the misleading conception that linear logic is more …
precision of linear logic, because of the misleading conception that linear logic is more …
Functorial string diagrams for reverse-mode automatic differentiation
M Alvarez-Picallo, DR Ghica, D Sprunger… - arXiv preprint arXiv …, 2021 - arxiv.org
We enhance the calculus of string diagrams for monoidal categories with hierarchical
features in order to capture closed monoidal (and cartesian closed) structure. Using this new …
features in order to capture closed monoidal (and cartesian closed) structure. Using this new …