Coalgebraic Quantum Computation

TL;DR

This paper introduces a coalgebraic framework for modeling quantum computation systems using convex sets of density matrices, enabling the reduction of quantum systems to simpler probabilistic models with equivalent behavior.

Contribution

It presents a novel coalgebraic representation of quantum systems, bridging quantum and probabilistic models in a unified mathematical framework.

Findings

Coalgebraic models can represent quantum systems using convex sets of density matrices.

Quantum systems can be transformed into equivalent probabilistic systems.

The method simplifies analysis of quantum systems by reducing complexity.

Abstract

Coalgebras generalize various kinds of dynamical systems occuring in mathematics and computer science. Examples of systems that can be modeled as coalgebras include automata and Markov chains. We will present a coalgebraic representation of systems occuring in the field of quantum computation, using convex sets of density matrices as state spaces. This will allow us to derive a method to convert quantum mechanical systems into simpler probabilistic systems with the same probabilistic behaviour.