Abstract
Model checking is a well-established and widely adopted framework used to verify whether a given system satisfies the desired properties. Properties are usually given by means of formulas from a specific logic; there are several logics that can be used, such as CTL and LTL, which permit the expression of different types of properties on the branching-time or on the linear-time evolution of the system. In this paper, we will consider the problem of model checking quantum systems and present the solutions given in literature for solving such a problem with respect to different types of properties.
Highlights
One of the main questions a designer needs to answer while developing a new system, being it a program, a protocol, or some hardware, is: how can I be sure my system works as expected? There are several ways to answer this question. Citation: Turrini, A
In this paper we have presented three logics and relative model checking algorithms for quantum Markov chains given in literature: quantum Computation Tree Logic (CTL), quantum Linear-time Temporal Logic (LTL) and ω-regular properties, and fidelity CTL
The former two kinds of properties focus on evaluating the probability of certain events; the latter, instead, looks for how well the super-operator modelled by the labelled quantum Markov chain (LQMC) preserves the quantum states it is applied on
Summary
One of the main questions a designer needs to answer while developing a new system, being it a program, a protocol, or some hardware, is: how can I be sure my system works as expected? There are several ways to answer this question. One can manually prove that the system is correct by applying the techniques learned in programming and cryptography courses, such as by using Hoare logic/triples to prove properties of programs or by showing that the cryptographic protocol is provably secure. This approach provides the desired guarantees, but it is tedious, error prone, and reasonably applicable only to very small systems. One can apply one of the several techniques developed by researches for this purpose, such as model checking, abstract interpretation, and high-order theorem proving These techniques can be usually applied automatically to the system and are able to scale to large systems.
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