arXiv subjects

Marie Lalire

Publications and source records attributed to Marie Lalire.

4 recordsLinked to original sources

arXiv2006

Relations among quantum processes: bisimilarity and congruence

Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and distributed quantum computations and quantum communication protocols, communications over quantum channels 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. This notation 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, an equivalence is defined among process states considered as having the same behavior. This equivalence is a probabilistic branching bisimulation. From this relation, an equivalence on processes is defined. However, it is not a congruence because it is not preserved by parallel composition.

quant-ph↗

arXiv2005

A probabilistic branching bisimulation for quantum processes

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.

quant-ph↗

arXiv2004

A Process Algebraic Approach to Concurrent and Distributed Quantum Computation: Operational Semantics

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, named QPAlg for Quantum Process Algebra, which provides a homogeneous style to formal descriptions of concurrent and distributed computations comprising both quantum and classical parts. On the quantum side, QPAlg provides quantum variables, operations on quantum variables (unitary operators and measurement observables), as well as new forms of communications involving the quantum world. The operational semantics makes sure that these quantum objects, operations and communications operate according to the postulates of quantum mechanics.

quant-ph↗

arXiv2003

Toward a Quantum Process Algebra

Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, 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. This paper aims at defining a high level language allowing the description of classical and quantum programming, and their cooperation. Since process algebras provide a framework to model cooperating computations and have well defined semantics, they have been chosen as a basis for this language. Starting with a classical process algebra, this paper explains how to transform it for including quantum computation. The result is a quantum process algebra with its operational semantics, which can be used to fully describe quantum algorithms in their classical context.

quant-ph↗