46 research outputs found
Operational Semantics and Type Soundness of Quantum Programming Language LanQ
We present an imperative quantum programming language LanQ which was designed
to support combination of quantum and classical programming and basic process
operations - process creation and interprocess communication. The language can
thus be used for implementing both classical and quantum algorithms and
protocols. Its syntax is similar to that of C language what makes it easy to
learn for existing programmers. In this paper, we present operational semantics
of the language and a proof of type soundness of the noncommunicating part of
the language. We provide an example run of a quantum random number generator.Comment: 71 pages, 16 figures; simulator available at http://lanq.sf.net
Reachability and Termination Analysis of Concurrent Quantum Programs
We introduce a Markov chain model of concurrent quantum programs. This model
is a quantum generalization of Hart, Sharir and Pnueli's probabilistic
concurrent programs. Some characterizations of the reachable space, uniformly
repeatedly reachable space and termination of a concurrent quantum program are
derived by the analysis of their mathematical structures. Based on these
characterizations, algorithms for computing the reachable space and uniformly
repeatedly reachable space and for deciding the termination are given.Comment: Accepted by Concur'12. Comments are welcom
Verification of Linear Optical Quantum Computing using Quantum Process Calculus
We explain the use of quantum process calculus to describe and analyse linear
optical quantum computing (LOQC). The main idea is to define two processes, one
modelling a linear optical system and the other expressing a specification, and
prove that they are behaviourally equivalent. We extend the theory of
behavioural equivalence in the process calculus Communicating Quantum Processes
(CQP) to include multiple particles (namely photons) as information carriers,
described by Fock states or number states. We summarise the theory in this
paper, including the crucial result that equivalence is a congruence, meaning
that it is preserved by embedding in any context. In previous work, we have
used quantum process calculus to model LOQC but without verifying models
against specifications. In this paper, for the first time, we are able to carry
out verification. We illustrate this approach by describing and verifying two
models of an LOQC CNOT gate.Comment: In Proceedings EXPRESS/SOS 2014, arXiv:1408.127
Formal Analysis of Quantum Systems using Process Calculus
Quantum communication and cryptographic protocols are well on the way to
becoming an important practical technology. Although a large amount of
successful research has been done on proving their correctness, most of this
work does not make use of familiar techniques from formal methods, such as
formal logics for specification, formal modelling languages, separation of
levels of abstraction, and compositional analysis. We argue that these
techniques will be necessary for the analysis of large-scale systems that
combine quantum and classical components, and summarize the results of initial
investigation using behavioural equivalence in process calculus. This paper is
a summary of Simon Gay's invited talk at ICE'11.Comment: In Proceedings ICE 2011, arXiv:1108.014
Application of Quantum Process Calculus to Higher Dimensional Quantum Protocols
We describe the use of quantum process calculus to describe and analyze
quantum communication protocols, following the successful field of formal
methods from classical computer science. We have extended the quantum process
calculus to describe d-dimensional quantum systems, which has not been done
before. We summarise the necessary theory in the generalisation of quantum
gates and Bell states and use the theory to apply the quantum process calculus
CQP to quantum protocols, namely qudit teleportation and superdense coding.Comment: In Proceedings QPL 2012, arXiv:1407.842
Open Bisimulation for Quantum Processes
Quantum processes describe concurrent communicating systems that may involve quantum information. We propose a notion of open bisimulation for quantum processes and show that it provides both a sound and complete proof methodology for a natural extensional behavioural equivalence between quantum processes. We also give a modal characterisation of open bisimulation, by extending the Hennessy-Milner logic to a quantum setting