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JUCS - Journal of Universal Computer Science

Towards a set of metrics for hybrid (quantum/classical) systems maintainability

Ana Díaz Muñoz, Moisés Rodríguez, Mario G. Piattini

Published Jan 22, 2024• 14 citations
Publisher

Abstract

Given the rapid evolution that has taken place in recent years in the software industry, and along with it the emergence of quantum software, there is a need to design an environment for measuring quality metrics for hybrid, classic-quantum software. In order to measure and evaluate the quality of classic software, there are models and standards, among which ISO/IEC 25000 stands out, which proposes a set of quality characteristics such as maintainability. However, there is currently no consensus for the measurement and evaluation of quantum software quality. In this paper we propose a series of adaptations to “classic” metrics, as well as a set of new measurements for hybrid maintainability. Finally, a first prototype of a measurement tool developed as a SonarQube plugin, capable of measuring these metrics in quantum developments, is also presented.

DOI
10.3897/jucs.99348

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Given the rapid evolution that has taken place in recent years in the software industry, and along with it the emergence of quantum software, there is a need to design an environment for measuring quality metrics for hybrid, classic-quantum software. In order to measure and evaluate the quality of classic software, there are models and standards, among which ISO/IEC 25000 stands out, which proposes a set of quality characteristics such as maintainability. However, there is currently no consensus for the measurement and evaluation of quantum software quality. In this paper we propose a series of adaptations to “classic” metrics, as well as a set of new measurements for hybrid maintainability. Finally, a first prototype of a measurement tool developed as a SonarQube plugin, capable of measuring these metrics in quantum developments, is also presented.
This doctoral dissertation, presented in the form of a compendium of publications, focuses on the design, implementation, and validation of an innovative model for evaluating analyz- ability—understood as a key subcharacteristic of maintainability—in the context of quantum software and, more broadly, hybrid software systems (those integrating classical and quantum components). In a landscape where quantum computing is rapidly advancing and beginning to consolidate in industrial applications, a pressing need arises to adapt and extend traditional software quality models, such as those established in the ISO/IEC 25000 family, to address the specific characteristics of quantum code. The lack of dedicated metrics hinders the rigorous evaluation of critical attributes like analyzability, negatively affecting hybrid systems’ maintainability, evolvability, and reliability in highly complex technical environments. The main objective of this dissertation is the design, implementation, and validation of an evaluation model focused on analyzability, which combines adapted classical metrics with newly defined indicators tailored explicitly for the quantum component. While the model targets hybrid systems, the validation has been exclusively focused on the quantum component, which constitutes the core contribution of this research. The classical part relies on well-established metrics validated and certified by bodies such as ILAC and ENAC and has therefore not been experimentally evaluated in this work. Additionally, an automated technological environment has been developed as a key element of the compendium, facilitating the practical application of the model in real-world projects. This environment enables integrated and real-time measurement of both classical and quantum metrics. However, like the model, its validation has been limited to the novel quantum indicators defined in this thesis. This approach strengthens the proposed methodology and lays the groundwork for future validation of the fully integrated hybrid model. The adopted methodology is grounded in an exhaustive review of the state of the art, the formal and informal definition of metrics, the development of the automated environment, and empirical validation through a family of experiments. The compendium of publications includes, among others, the following articles: Towards a set of metrics for hybrid (quan- tum/classical) systems maintainability, Implementing an environment for hybrid software evaluation, and Environment for the Evaluation of Hybrid (Classical-Quantum) Systems Analyzability. As part of the validation process, a preliminary study has been accepted at the international conference IQSOFT 2025, and an extended version has been submitted to the journal Empirical Software Engineering (EmSE), and is currently under review. The results demonstrate that the proposed model enables precise quantification of quantum software analyzability and that its application in hybrid systems is feasible conceptually and technically. The developed technological environment supports reproducible and systematic evaluation, laying a foundation for future applications in hybrid software engineering. The em- pirical validation conducted thus far has been deliberately limited to the quantum component, given that classical metrics are already widely established and certified. In conclusion, this dissertation represents a significant advance in the evaluation of hybrid software quality. It proposes a validated model that contributes to strengthening maintain- ability and supporting the evolution of complex systems in an ever-changing technological landscape.
As quantum computing evolves, the demand for high-quality quantum software is increasing. Classical software quality models, such as McCall's model, provide a useful foundation, but they do not explicitly capture distinctive properties of quantum software, including probabilistic measurement outcomes, backend-dependent behavior, and hybrid quantum-classical workflows. This paper proposes a base quality model for quantum software using McCall's factor-criterion-metric structure as the organizing backbone. It broadens the set of quality factors by drawing on representative classical software quality models and standards and introduces quantum-specific extensions only where needed. We define the resulting factor set and quality criteria, provide a many-to-many mapping of core factor-to-criterion relationships, discuss representative candidate metrics together with the execution, reference, and interpretation conditions needed to use them, and illustrate how the resulting model can be applied across the quantum software lifecycle. The model is intended as a common starting point for structuring, assessing, and communicating quality concerns in quantum software while supporting context-specific adaptation. Further expert feedback, case studies, and empirical studies can be used to evaluate and refine the model and its application across different quantum software contexts.
Quantum computing is the basis of a new revolution. Several quantum computers are already available and, with them, quantum programming languages, quantum software development kits and platforms, quantum error correction and optimization tools are proposed and presented continuously. In connection with this, disciplines such as the Quantum Software Engineering are appearing for applying the knowledge acquired through time in their corresponding classical relatives. Besides, measurement is well known as a key factor for assessing, and improving if needed, the quality of any model in terms of, for instance, its understandability. The easier to understand a model is, the easier to maintain, reuse, etc. In this work, we present the definition of a set of metrics for assessing the understandability of quantum circuits. Some examples of the calculation of the metrics are also presented. This is just the beginning of a more thorough process in which they will be empirically validated by the performance of empirical studies, especially experiments.
Rapid growth in quantum computing has created an urgent need to adapt traditional software engineering methodologies. Among these methodological challenges, software size measurement plays a central role in project estimation, quality assurance, and software engineering management. However, there is no consolidated understanding of how it should be applied to quantum software systems. This paper presents the first systematic literature review on quantum software size measurement, synthesizing existing approaches, and identifying key research gaps. An analysis of 16 studies shows that size measures span multiple abstraction levels, with most research focusing on adapting classical metrics, such as Lines of Code (LOC) and functional size, to quantum software systems. LOC continues to be used for sizing quantum code, while COSMIC Function Points (ISO 19761) have been extended to capture data movements in quantum components, enabling their application at the requirement, code, and circuit levels. At the specification and architectural design levels, the proposed measures include counts of quantum classes and methods as well as lines of architectural specifications. At the circuit level, quantum-specific constructs, such as qubits, gates, and measurements, are also incorporated. Additionally, software structure metrics, including cyclomatic complexity and Halstead metrics, are used to measure quantum software at both the code and design levels. Research output has grown since 2024, and is driven by academic groups, with minimal industrial participation. However, most metrics remain conceptual, lack empirical validation, and are not integrated into development life cycles, highlighting the immaturity and fragmentation of current proposals and the need for standardized frameworks.
In the context of quantum-classical hybrid computing, evaluating analysability, which is the ease of understanding and modifying software, presents significant challenges due to the complexity and novelty of quantum algorithms. Although advances have been made in quantum software development, standard software quality evaluation methods do not fully address the specifics of quantum components, resulting in a gap in the ability to ensure and maintain the quality of hybrid software products. In this registered report proposal, we intend to validate a quality model focused on the analysability of hybrid software through an international collab orative approach involving academic institutions from Italy and Spain through a controlled experiment. This approach allows for a more detailed analysis and validation methodology and establishes a framework for future research and developments in software quality assessment in quantum computing.
Abstract Developers of the many promising quantum computing applications that currently exist are urging companies in many different sectors seriously consider integrating this new technology into their business. For these applications to function, not only are quantum computers required, but quantum software also. Accordingly, quantum software engineering has become an important research field, in that it attempts to apply or adapt existing methods and techniques (or propose new ones) for the analysis, design, coding, and testing of quantum software, as well as playing a key role in ensuring quality in large-scale productions. The design of quantum software nevertheless poses two main challenges: the modelling of software quantum elements must be done in high-level modelling languages; and the need to further develop so-called “hybrid information systems”, which combine quantum and classical software. To address these challenges, we first propose a quantum UML profile for analysing and designing hybrid information systems; we then demonstrate its applicability through various structural and behavioural diagrams such as use case, class, sequence, activity, and deployment. In comparison to certain other quantum domain-specific languages, this UML profile ensures compliance with a well-known international standard that is supported by many tools and is followed by an extensive community.