A probabilistic branching bisimulation for quantum processes

TL;DR

This paper introduces a process algebra framework for modeling concurrent quantum and classical computations, incorporating quantum communication and a probabilistic bisimulation to analyze process equivalence.

Contribution

It develops a homogeneous process algebraic notation and a probabilistic branching bisimulation for quantum processes, integrating quantum mechanics principles into formal process modeling.

Findings

Defines a process algebra for quantum-classical systems

Establishes a probabilistic bisimulation for quantum processes

Ensures quantum operations adhere to quantum mechanics postulates

Abstract

Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate.Moreover, to model concurrent and distributed quantum computations, as well as quantum communication protocols, quantum to quantum communications which move qubits physically from one place to another must also be taken into account. Inspired by classical process algebras, which provide a framework for modeling cooperating computations, a process algebraic notation is defined, which provides a homogeneous style to formal descriptions of concurrent and distributed computations comprising both quantum and classical parts.Based upon an operational semantics which makes sure that quantum objects, operations and communications operate according to the postulates of quantum mechanics, a probabilistic branching bisimulation is defined among processes considered as having the same behavior.