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Register a new userFormal Methods for Quantum Programs: A Survey
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Added by
Christophe Chareton
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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While recent progress in quantum hardware open the door for significant speedup in certain key areas (cryptography, biology, chemistry, optimization, machine learning, etc), quantum algorithms are still hard to implement right, and the validation of such quantum programs is achallenge. Moreover, importing the testing and debugging practices at use in classical programming is extremely difficult in the quantum case, due to the destructive aspect of quantum measurement. As an alternative strategy, formal methods are prone to play a decisive role in the emerging field of quantum software. Recent works initiate solutions for problems occurring at every stage of the development process: high-level program design, implementation, compilation, etc. We review the induced challenges for an efficient use of formal methods in quantum computing and the current most promising research directions.
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In todays world, critical infrastructure is often controlled by computing systems. This introduces new risks for cyber attacks, which can compromise the security and disrupt the functionality of these systems. It is therefore necessary to build such systems with strong guarantees of resiliency against cyber attacks. One way to achieve this level of assurance is using formal verification, which provides proofs of system compliance with desired cyber security properties. The use of Formal Methods (FM) in aspects of cyber security and safety-critical systems are reviewed in this article. We split FM into the three main classes: theorem proving, model checking and lightweight FM. To allow the different uses of FM to be compared, we define a common set of terms. We further develop categories based on the type of computing system FM are applied in. Solutions in each class and category are presented, discussed, compared and summarised. We describe historical highlights and developments and present a state-of-the-art review in the area of FM in cyber security. This review is presented from the point of view of FM practitioners and researchers, commenting on the trends in each of the classes and categories. This is achieved by considering all types of FM, several types of security and safety critical systems and by structuring the taxonomy accordingly. The article hence provides a comprehensive overview of FM and techniques available to system designers of security-critical systems, simplifying the process of choosing the right tool for the task. The article concludes by summarising the discussion of the review, focusing on best practices, challenges, general future trends and directions of research within this field.
Building upon recent work on probabilistic programs, we formally define the notion of expected runtime for quantum programs. A representation of the expected runtimes of quantum programs is introduced with an interpretation as an observable in physics. A method for computing the expected runtimes of quantum programs in finite-dimensional state spaces is developed. Several examples are provided as applications of this method; in particular, an open problem of computing the expected runtime of quantum random walks is solved using our method.
Practical error analysis is essential for the design, optimization, and evaluation of Noisy Intermediate-Scale Quantum(NISQ) computing. However, bounding errors in quantum programs is a grand challenge, because the effects of quantum errors depend on exponentially large quantum states. In this work, we present Gleipnir, a novel methodology toward practically computing verified error bounds in quantum programs. Gleipnir introduces the $(hatrho,delta)$-diamond norm, an error metric constrained by a quantum predicate consisting of the approximate state $hatrho$ and its distance $delta$ to the ideal state $rho$. This predicate $(hatrho,delta)$ can be computed adaptively using tensor networks based on the Matrix Product States. Gleipnir features a lightweight logic for reasoning about error bounds in noisy quantum programs, based on the $(hatrho,delta)$-diamond norm metric. Our experimental results show that Gleipnir is able to efficiently generate tight error bounds for real-world quantum programs with 10 to 100 qubits, and can be used to evaluate the error mitigation performance of quantum compiler transformations.
Program transformation is an appealing technique which allows to improve run-time efficiency, space-consumption, and more generally to optimize a given program. Essentially, it consists of a sequence of syntactic program manipulations which preserves some kind of semantic equivalence. Unfolding is one of the basic operations which is used by most program transformation systems and which consists in the replacement of a procedure call by its definition. While there is a large body of literature on transformation and unfolding of sequential programs, very few papers have addressed this issue for concurrent languages. This paper defines an unfolding system for CHR programs. We define an unfolding rule, show its correctness and discuss some conditions which can be used to delete an unfolded rule while preserving the program meaning. We also prove that, under some suitable conditions, confluence and termination are preserved by the above transformation. To appear in Theory and Practice of Logic Programming (TPLP)
Industrial automation systems (IAS) need to be highly dependable; they should not merely function as expected but also do so in a reliable, safe, and secure manner. Formal methods are mathematical techniques that can greatly aid in developing dependable systems and can be used across all phases of the system development life cycle (SDLC), including requirements engineering, system design and implementation, verification and validation (testing), maintenance, and even documentation. This state-of-the-art survey reports existing formal approaches for creating more dependable IAS, focusing on static formal methods that are used before a system is completely implemented. We categorize surveyed works based on the phases of the SDLC, allowing us to identify research gaps and promising future directions for each phase.
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