194 citations · 1.2k across the 78 of their papers we have counts for
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Categorical Quantum Mechanics I: Causal Quantum Processes
Bob Coecke, Aleks Kissinger
We derive the category-theoretic backbone of quantum theory from a process ontology. More specifically, we treat quantum theory as a theory of systems, processes and their interact…
Generalised Compositional Theories and Diagrammatic Reasoning
Bob Coecke, Ross Duncan, Aleks Kissinger +1
This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We ill…
A first-order logic for string diagrams
Aleks Kissinger, David Quick
Equational reasoning with string diagrams provides an intuitive means of proving equations between morphisms in a symmetric monoidal category. This can be extended to proofs of inf…
Equational reasoning with context-free families of string diagrams
Aleks Kissinger, Vladimir Zamdzhiev
String diagrams provide an intuitive language for expressing networks of interacting processes graphically. A discrete representation of string diagrams, called string graphs, allo…
Tensors, !-graphs, and non-commutative quantum structures (extended version)
Aleks Kissinger, David Quick
!-graphs provide a means of reasoning about infinite families of string diagrams and have proven useful in manipulation of (co)algebraic structures like Hopf algebras, Frobenius al…
Quantomatic: A Proof Assistant for Diagrammatic Reasoning
Aleks Kissinger, Vladimir Zamdzhiev
Monoidal algebraic structures consist of operations that can have multiple outputs as well as multiple inputs, which have applications in many areas including categorical algebra,…