resources used throughout the software life cycle. It examines several published works that analyze quantum software

modelling in the context of the various phases of the life cycle, from analysis/requirements to testing and maintenance.

Each annotation provides an analysis of software engineering resources applicable to quantum software development

and their applicability to different phases of the software development process. By synthesizing these diverse

perspectives, this bibliography illuminates the evolving landscape of quantum software development and underscores

(*) Corresponding Author.

to the design, development of computer programs and the associated documentation required to develop, operate and

Engineering as the establishment of engineering principles and methods for obtaining costeffective software that is

reliable and works on real machines. Then in 1993, the IEEE synthesised it as the application of a systematic, disciplined

At its core, software engineering addresses the challenges associated with creating and maintaining complex and

reliable software systems. This involves carrying out activities such as requirements specification, architectural design,

code implementation, software testing, configuration management, project management and software quality

assurance.

mechanics to process information in a radically different way from classical computing [6]. Unlike classical bits, which

can be in one of two states (0 or 1) at any time, quantum qubits can exist in multiple states simultaneously [7], thanks

to a phenomenon known as quantum superposition. This allows quantum computing to explore a much wider range of

One of the fundamental concepts in quantum computing is quantum entanglement, which allows two or more qubits

to be intrinsically related so that the state of one is instantaneously correlated with the state of the other, regardless of

the distance between them. This leads to a phenomenon known as quantum teleportation, where information can be

transferred between distant qubits without requiring physical transmission of the information through space [8].

Despite its potential, quantum computing is still in its early stages of development and faces numerous technical

challenges, such as the need to build more robust and stable qubits, develop effective quantum error correction

techniques and build scalable hardware architectures. However, recent advances in the field have generated great

interest and optimism in the scientific and technological community, and quantum computing is expected to play a

transformative role in solving some of the most complex challenges in computing and science in the decades to come

[10].

Quantum computing represents an innovative way of processing information by exploiting the principles of quantum

mechanics. These computing systems, based on units of information called qubits, operate in a superposition state,

allowing them to perform calculations simultaneously in multiple states. Quantum algorithms are algorithms designed

representations of sequences of quantum operations that transform a set of input qubits into a desired result. These

revolutionize the way we process information, and its potential impact extends to a wide range of fields, from

cryptography and artificial intelligence to molecular simulation and process optimization. In this context, modelling

plays a crucial role in providing tools and methodologies to represent and understand quantum systems more accurately

and effectively. Through modelling, researchers and developers can capture the complex phenomena underlying

quantum computation, explore new possibilities for quantum algorithms and circuits, and design more efficient and

applied to Quantum Computing. This review is inspired by the work of kitchenham [11] where we will focus on

examining how different modelling approaches are being used to advance the field of quantum computing, identifying

the challenges and opportunities they face and exploring their potential to drive the next generation of quantum

To address this challenge, it is essential to develop higher-level software engineering resources that hide the underlying

complexity and allow developers to focus on business logic and problem solving [12]. This includes creating more

intuitive programming languages and software abstractions that simplify interaction with quantum systems. In addition,

there is a need to develop libraries and frameworks that provide common functions and development tools for tasks

such as simulation, debugging and optimization of quantum algorithms.

By favoring the development of quantum or mixed systems, where parts of the system are quantum and others are

traditional [10], these software engineering resources can pave the way for the wider adoption of quantum computing

in a variety of applications and industry sectors. By enabling a broader set of developers to harness the power of

quantum computing without requiring a deep understanding of the underlying physics, these tools have the potential

system requirements, facilitating clearer and more effective communication between team members and ensuring a

shared understanding of the project.

The advantage of using abstract models in building quantum software lies in their ability to simplify the inherent

complexity of quantum systems. By representing the essential aspects of the system in a clear and concise manner,

abstract models allow developers to approach complex problems more systematically and effectively. Furthermore, by

separating the specification of the system from its implementation, abstract models make it easier to adapt the software

as requirements or technologies evolve, ensuring that the system is flexible and can be easily maintained over time.

In summary, the use of abstract models in building quantum software offers a number of significant benefits, including

models, organizations can develop quantum software more efficiently and effectively, driving the adoption and

software modelling, elucidating the intricate interplay between quantum principles and established software

engineering practices.

First, we will write a brief summary of each work, and then we will review the collection to identify a) which software

engineering resources they contribute and b) at which stage of the software development lifecycle they are applied.

The paper presents a set of Abstract Patterns for Quantum programming. These are de list of patterns proposed:

2. (2020) [14] Towards a Quantum Software Modeling Language, (2022) [15] Design of classical-quantum systems

with UML also in [16] Chapter 6: A quantum software modeling language:

In these works, the authors introduce the concept of Quantum software modelling by expressing that Quantum

Computing is based on the counter-intuitive principles of quantum mechanics [7], such as superposition and

entanglement, among others. Thus, lessons learned from existing and classical design techniques cannot simply be

applied [9], but new quantum foundations and features have to be devised. In this sense, quantum software is currently

still coded manually and ad hoc. For example, although there are some well-known algorithms that are defined in the

literature using mathematical formalism, these algorithms have been hand-coded in multiple ways for specific quantum

analyzed and designed together, which in itself poses another major challenge.

The main contribution of this work is to provide a quantum UML profile that covers the main modelling aspects of the

analysis and design of hybrid information systems. The quantum UML profile also covers structural and behavioral

aspects. In particular, it addresses use cases, class, sequence, activity and deployment diagrams. As a result, both

quantum and classical elements, as well as the relationships between them, can be modelled together in an integrated

design.

It has a special section discussing Quantum Software Design, where different approaches are mentioned.

3. (2020) [17] Software engineering for ’quantum advantage’:

This paper argues for the need for a proper quantum software engineering discipline benefiting from precise

foundations and calculi, capable of supporting algorithm development and analysis.

They identify the following main issues around which any roadmap for a Software Engineering discipline should take

how properties of their behaviors are anticipated, expressed and verified.

6. (2020) [20] Modeling Quantum programs: Challenges, initial results, and research directions:

The paper defines the concepts of high-level abstraction (platform independent) modeling language development.

Proposes a quantum modeling approach at multiple levels of abstraction, class diagramming, flows and state machine.

Presents an example of quantum entanglement modeling. It also proposes some lines of action and open issues

involving Quantum Software Modeling Notations and Methodologies, Quantum Constraint Specification, Quantum

7. (2021) [21] Towards Model-Driven Quantum Software Engineering:

This work explores the use of Model Driven Engineering (MDE) on quantum technologies by means of an intermediate

This paper claims that there should be just a single unified and rigorous design procedure for both classical and

quantum software systems.

The main contribution of this paper is the unified linear algebra design approach to classical and quantum software

systems, starting from their representation as design Density Matrices.

9. (2022) [22] A Model-Driven Framework for Composition-Based Quantum Circuit Design:

In this pre-print they propose a composition-oriented modelling language for creating quantum circuits together with

a modelling framework which (i) allows for a flexible and convenient definition and application of composite

10. (2022) [24] Software Architecture for Quantum Computing Systems – A Systematic Review:

The objective of this review is to complement Software Engineering based studies and specifically focus on

be useful if we relate it to Quantum-Classical hybrid computing. This work has many good references and covers all

It is important to mention that in modeling topics, the author Khan et al. refers to the same works that we analyze,

which are: [18], [13] [14]. We identified in this work some definitions and concepts related to modeling. Architectural

process and activities: An architecture design endeavour for the quantum software requires an architecting process to

incorporate a number of architecting activities. Existing architectural process can be leveraged to support five

architecting activities for quantum software namely (i) architectural requirements, (ii) architectural modelling, (iii)

Architectural modelling notations: Modelling notations to specify quantum software architectures primarily rely on

box and arrow notations (having component diagrams) and graph-based models (having state graph) to represent the

structures and behaviour of quantum software under design. Unlike conventional software architectures that mostly

Layered and pipe and filter patterns are identified as the most recurring quantum software architecture patterns.

However, these are generic or classical patterns that can be used to design any software system. To this end, further

research efforts are required to explore and propose new patterns to particularly focus on quantum computing attributes

(e.g., superposition and quantum entanglement) and facilitate the architecture of quantum software systems.

As said the paper is a good starting point to find references to other primary works that focus on different topics related

to Quantum Software design and Quantum Architectures.

11. (2023) [25] Model-Driven Optimization for Quantum Program Synthesis with MOMoT:

This paper presents how MDO approaches, in particular MOMoT framework, can be applied to the problem of

This article proposes a unified metamodel for modelling quantum circuits, together with five strategies for its use and

some examples of its application. The article also provides a set of constraints (OCL) for using the identified strategies,

a set of procedures for transforming the models between the strategies, and an analysis of the suitability of each strategy

for performing common tasks in a model-driven quantum software development environment.

The metamodel extends the well-known metamodel of graphs (direct-acyclic graphs) to combine all the approaches

into a single modelling language.

This makes it possible to support different modelling strategies and the transformations that can be applied between

them based on the Node concept. In short, the Node provides the developer with the necessary flexibility to decide

section of the circuit.

said transformation has been applied to a model.

In the paper, the authors present a kind of taxonomical view of the fundamental concepts of quantum computing and

review only intends to detect the fundamental concepts of quantum computing and quantum software as an starting

point to address the study of this discipline. The paper introduces the concepts of quantum computing and builds an

interesting body of Knowledge (BOK).

14. (2023) [28] Formalization of Quantum Intermediate Representations for Code Safety:

This work proposes the formal definition of a generic reusable compilation tool (qIRs, intermediate representations)

based on LLVM and applicable on different frontend languages and back-end hardware platforms. It formally defines

syntax and semantics and an intermediate code conversion.

15. (2023) [29] ScaffML: A Quantum Behavioral Interface Specification Language for Scaffold:

This paper proposes the use of a behavioral interface specification language (BISL) called ScaffML for the quantum

programming language Scaffold to specify behavior and interface of programs, modules, prepostconditions and

assertions.

optimization strategies for each specific platform based on the analysis of these Hamiltonians, which makes it possible

to bring the simulated performance closer to the real performance on that platform. SimuQ generates executable pulse

schedules for real devices to simulate the evolution of desired quantum systems, which is demonstrated on

superconducting (IBM), neutral-atom (QuEra), and trapped-ion (IonQ) quantum devices.

strategies they employ in the realm of quantum software modelling. By categorizing the papers according to their

chosen design strategies, we aim to provide readers with a comprehensive overview of the diverse methodologies

the groundwork for future exploration and innovation in this rapidly evolving domain.