The Many-Worlds Calculus
Logic in Computer Science
2025-05-21 v6 Quantum Physics
Abstract
In this paper, we explore the interaction between two monoidal structures: a multiplicative one, for the encoding of pairing, and an additive one, for the encoding of choice. We propose a colored PROP to model computation in this framework, where the choice is parameterized by an algebraic side effect: the model can support regular tests, probabilistic and non-deterministic branching, as well as quantum branching, i.e. superposition. The graphical language comes equipped with a denotational semantics based on linear applications, and an equational theory. We prove the language to be universal, and the equational theory to be complete with respect to this semantics.
Cite
@article{arxiv.2206.10234,
title = {The Many-Worlds Calculus},
author = {Kostia Chardonnet and Marc de Visme and Benoît Valiron and Renaud Vilmart},
journal= {arXiv preprint arXiv:2206.10234},
year = {2025}
}