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Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning
TLDR
This entirely diagrammatic presentation of quantum theory represents the culmination of ten years of research, uniting classical techniques in linear algebra and Hilbert spaces with cutting-edge developments in quantum computation and foundations.
Picturing Quantum Processes
The Compositional Structure of Multipartite Quantum Entanglement
TLDR
It is shown that multipartite quantum entanglement admits a compositional structure, and hence is subject to modern computer science methods, and induces a generalised graph state paradigm for measurement-based quantum computing.
Quantomatic: A proof assistant for diagrammatic reasoning
TLDR
This work briefly outlines the theoretical basis of Quantomatic's rewriting engine, then gives an overview of the core features and architecture and gives a simple example project that computes normal forms for commutative bialgebras.
Open-graphs and monoidal theories†
  • L. Dixon, A. Kissinger
  • Mathematics, Computer Science
    Mathematical Structures in Computer Science
  • 18 November 2010
TLDR
This paper introduces the notion of a selective adhesive functor, and shows that such a functor embeds the category of open-graphs into the ambient adhesive category of typed graphs, and inherits ‘enough adhesivity’ from the categoryof typed graphs to perform double-pushout (DPO) graph rewriting.
ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity
We present a new graphical calculus that is sound and complete for a universal family of quantum circuits, which can be seen as the natural string-diagrammatic extension of the approximately
CNOT circuit extraction for topologically-constrained quantum memories
TLDR
A new technique for quantum circuit mapping, based on Gaussian elimination constrained to certain optimal spanning trees called Steiner trees, is given, which significantly out-performs general-purpose routines on CNOT circuits.
Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus
TLDR
A simplification strategy for ZX-diagrams is given based on the two graph transformations of local complementation and pivoting and it is shown that the resulting reduced diagram can be transformed back into a quantum circuit.
Strong Complementarity and Non-locality in Categorical Quantum Mechanics
TLDR
The diagrammatic calculus substantially simplifies (and sometimes even trivialises) many of the derivations, and provides new insights, and the diagrammatic computation of correlations clearly shows how local measurements interact to yield a global overall effect.
PyZX: Large Scale Automated Diagrammatic Reasoning
TLDR
This paper introduces PyZX, an open source library for automated reasoning with large ZX-diagrams, and shows how PyZX implements methods for circuit optimisation, equality validation, and visualisation and how it can be used in tandem with other software.
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