143 research outputs found
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
Observational Equivalence Using Schedulers for Quantum Processes
In the study of quantum process algebras, researchers have introduced
different notions of equivalence between quantum processes like bisimulation or
barbed congruence. However, there are intuitively equivalent quantum processes
that these notions do not regard as equivalent. In this paper, we introduce a
notion of equivalence named observational equivalence into qCCS. Since quantum
processes have both probabilistic and nondeterministic transitions, we
introduce schedulers that solve nondeterministic choices and obtain probability
distribution of quantum processes. By definition, the restrictions of
schedulers change observational equivalence. We propose some definitions of
schedulers, and investigate the relation between the restrictions of schedulers
and observational equivalence.Comment: In Proceedings QPL 2014, arXiv:1412.810
Symbolic bisimulation for quantum processes
With the previous notions of bisimulation presented in literature, to check
if two quantum processes are bisimilar, we have to instantiate the free quantum
variables of them with arbitrary quantum states, and verify the bisimilarity of
resultant configurations. This makes checking bisimilarity infeasible from an
algorithmic point of view because quantum states constitute a continuum. In
this paper, we introduce a symbolic operational semantics for quantum processes
directly at the quantum operation level, which allows us to describe the
bisimulation between quantum processes without resorting to quantum states. We
show that the symbolic bisimulation defined here is equivalent to the open
bisimulation for quantum processes in the previous work, when strong
bisimulations are considered. An algorithm for checking symbolic ground
bisimilarity is presented. We also give a modal logical characterisation for
quantum bisimilarity based on an extension of Hennessy-Milner logic to quantum
processes.Comment: 30 pages, 7 figures, comments are welcom
An Algebra of Quantum Processes
We introduce an algebra qCCS of pure quantum processes in which no classical
data is involved, communications by moving quantum states physically are
allowed, and computations is modeled by super-operators. An operational
semantics of qCCS is presented in terms of (non-probabilistic) labeled
transition systems. Strong bisimulation between processes modeled in qCCS is
defined, and its fundamental algebraic properties are established, including
uniqueness of the solutions of recursive equations. To model sequential
computation in qCCS, a reduction relation between processes is defined. By
combining reduction relation and strong bisimulation we introduce the notion of
strong reduction-bisimulation, which is a device for observing interaction of
computation and communication in quantum systems. Finally, a notion of strong
approximate bisimulation (equivalently, strong bisimulation distance) and its
reduction counterpart are introduced. It is proved that both approximate
bisimilarity and approximate reduction-bisimilarity are preserved by various
constructors of quantum processes. This provides us with a formal tool for
observing robustness of quantum processes against inaccuracy in the
implementation of its elementary gates
Bisimulation for quantum processes
In this paper we introduce a novel notion of probabilistic bisimulation for
quantum processes and prove that it is congruent with respect to various
process algebra combinators including parallel composition even when both
classical and quantum communications are present. We also establish some basic
algebraic laws for this bisimulation. In particular, we prove uniqueness of the
solutions to recursive equations of quantum processes, which provides a
powerful proof technique for verifying complex quantum protocols.Comment: Journal versio
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