Skills Required for Quantum Computing: A Comprehensive Review of Recent Studies

Abstract

Quantum mechanics as the basis of quantum computing imposes an inherent complexity for practitioners not formed on quantum physics, for understanding such new paradigm of computation and getting involved in the prominent quantum world. Strong technical skills on quantum topics, mathematics and related disciplines are required to attend job positions in the labor market. Furthermore, the multidisciplinary environment where quantum computing is immersed requires soft skills to work in integrative teams. This paper presents a literature review, supported by the systematic mapping methodology, to gather the core knowledge and technical skills, as well as soft skills required to prepare students and practitioners to work on quantum computing. The results allow us to have a wide spectrum of the competences involved, enabling academic institutions and educational bodies to design individual courses or curricula blocks to prepare the workforce.

INTRODUCTION

Quantum computing (QC) is currently one of the most promising approaches to empower the computing world [1–9]. Based on the effects of quantum mechanics (e.g., superposition, entanglement, and measurement), it may lead to a completely new range of solutions. The potential of QC is big for solving complex problems that classical computing cannot [1, 4]. QC is based on quantum mechanics principles [9–11]; its implementation involves a mathematical representation, as well as a probabilistic behavior of qubits and their treatment.

In this section, we summarize the main difficulties that quantum computing represents for practitioners with computer science formation and especially for software engineers. Also, we describe the purpose of this study and its realization.

Difficulties That Quantum Computing Represents for Practitioners

The quantum nature of QC makes it not accessible to non-physics specialists. Quantum computing has a strong influence from quantum mechanics as well as mathematics. Quantum computing involves the following fundamental concepts from quantum mechanics and mathematics [5, 10, 12, 13]:

(1) quantum mechanics: superposition, entanglement, quantum interference, measurement;

(2) quantum qubits and quantum states;

(3) quantum gates and quantum circuits;

(4) linear algebra (vector spaces, matrices, Eigenvalues and Eigenvectors);

(5) complex numbers;

(6) probability theory;

(7) tensor products;

(8) fourier transforms.

These sets of knowledge make quantum computing seem more complicated than classical computing. Because of this, programmers may face complications in conceptualizing and implementing quantum software.

The basic mathematical framework for quantum mechanics–the behavior of tiny particles of matter– was originally developed in the early part of the 20th century by Niels Bohr [14], Werner Heisenberg [15], Erwin Schrödinger [16], and Paul Dirac [17], among others. Now, 100 years later, in 2024 it is important to investigate how organizations and institutions are beginning to explore a fundamentally different type of computer, capable of exploiting these remarkable physical properties to tackle problems that would otherwise remain intractable.

Multidisciplinary approach for quantum computing. Related fields to QC are quantum information science (QIS) and quantum information science and technology (QIST). These two fields are closely related, the second one encompasses technology creation and management. QIS is an exciting field that draws from information theory, computer science, and quantum mechanics to process information in fundamentally new ways [18].

Cross disciplinary teams are applying QIS to new quantum technologies in communications, networking, data security, navigation, and medical diagnostics [11, 19, 20]. They are also making headway in developing quantum computing systems that may allow us to tackle challenges previously out of reach, in areas such as cryptography, logistics optimization, and across the natural sciences.

QIS itself could represent a new mindset for software developers because of the involvement of quantum principles.

The current deficit of specialists trained in quantum computing. QC has become more and more important for computer science and related fields (e.g., applied physics [21] or computational chemistry [22]) in recent years. Much research is currently being invested to make progress in developing new technologies and approaches [23]. One of the biggest problems is the high complexity of QC, especially in mathematics and physics, which leads to poor accessibility for computer scientists and software engineers [24].

There is evidence of the deficit of well-trained specialists in quantum computing. Currently, there are many bugs in infrastructural scripts and glue code [25]. There is a need for better language support to prevent bugs in quantum software components. Also, there is a need for well-trained programmers to implement quantum software and supporting platforms. Until today there are noncomputer science graduates working as quantum developers such as physics specialists [25], who require strong classical software engineering skills, such as more effective integration testing.

Today there are very few training programs in quantum computing, and there is no consensus on the curriculum structure. Most QC specialists are trained in noncomputing fields like physics, chemistry, or mathematics [26].

Several studies from industry labor market have revealed that there is a lack of the required skills and knowledge for quantum software [27]. This goes along with changes to implement in software engineering (SE) and education [23]. Current students are going to be the professionals of the future in the quantum computing labor market. Therefore, students of computer science must build up some new technical competencies in QC and surrounding fields (e.g., physics) to understand the characteristics of SE for QC.

Addressing the Problem

Quantum software development is a rapidly evolving field that aims to harness the power of quantum computing for various applications [3, 28–32]. Quantum computers use quantum bits, or qubits, that can exist in superpositions of two states, allowing them to perform complex calculations faster and more efficiently than classical computers [30]. However, quantum software development also faces many challenges, such as noise, error correction, scalability, and interoperability [28, 29, 32].

It is required that quantum technology vendors should make efforts that align with the quantum software engineering principles, providing industry with enough tools and trained people to struggle the lack of a skilled workforce [3].

To succeed in the industry, quantum software programmers need to know [33]:

(1) the complete details of the problem they are trying to solve;

(2) how to write quantum code;

(3) how to write solutions to their problem in quantum code;

(4) depending on the use case, how to write scalable quantum solutions.

Based on this, it is important to precise the knowledge and skills that quantum computing practitioners should have, especially quantum software engineers, to cover the requirements from quantum industry. Therefore, the objectives of this study are:

(1) identifying the competences required in quantum software industry, emphasizing the knowledge and skills that quantum computing practitioners must possess.

(2) identifying essential concepts for future curricular and educator activities that will help learners engage with quantum information science.

The rest of this paper is organized as follows. Section 2 contains a background, including needs of industry in terms of competences, skills, and abilities in quantum technologies. Section 3 contains some related work, citing educational efforts for preparing and training students on these competences. Section 4 describes the methodology used for reviewing the literature, emphasizing the steps for performing the systematic mapping. Section 5 exposes the results from the literature review, emphasizing three main elements: fundamental knowledge for quantum computing, technical or hard skills required, and soft skills required. Section 6 presents the discussion of the results, emphasizing main and specific findings. Section 7 contains the conclusions and future work. Finally, a section of references is presented, as well as three appendixes with complementary materials.

BACKGROUND

Educational bodies should attempt to address the lack of skilled professionals in the context of quantum computing and quantum software engineering. The new syllabus must clearly specify which competencies and skills are required for future quantum software engineers [3]. So that, syllabus should consider skills and abilities required in quantum software development for students [34]. The participation of different stakeholders such as professionals across industry, academia, and government who need new skills to capitalize on quantum computing [1] is required to address this issue in a better way.

Some efforts have been made to address this issue. Next, some of them are described.

Needs of the quantum industry. Hughes et al. [35], presented a report on the results from a survey of 57 companies in the quantum industry, with the goal of elucidating the jobs, skills, and degrees that are relevant for this new workforce.

This study intended to support the education and training of quantum workforce, arguing that universities and colleges require knowledge of the type of jobs available for their students and what skills and degrees are most relevant for those new jobs. This research question was formulated: What are these jobs, skills, and degrees demanded?

Findings: A range of job opportunities was found from highly specific jobs, such as quantum algorithm developer and error correction scientist, to broader jobs categories within the business, software, and hardware sectors. These broader jobs require a range of skills, most of which are not quantum related. Furthermore, except for the highly specific jobs, companies that responded to the survey are looking for a range of degree levels to fill these new positions, from bachelor to master and PhDs, mainly the last two ones.

Seven job positions explicitly require skills in quantum computing:

(1) Error correction scientist: Error correction, quantum algorithm development, quantum science (Chemistry, Physics, etc.).

(2) Experimental physicist: Quantum photonics/laser physics, quantum science (chemistry, physics, etc.), quantum sensor physics.

(3) Theoretical physicist: Quantum algorithm development, quantum science (chemistry, physics, etc.).

(4) Computational chemist: Quantum algorithm development, quantum science (chemistry, physics, etc.).

(5) Photonics/optics engineer/scientist: Quantum photonics/laser physics.

(6) Quantum algorithm developer: Quantum algorithm development.

(7) Application/solution architect: Quantum algorithm development.

With this information reported by Hughes et al. [35], students, instructors, and university administrators can make informed decisions about how to address the challenge of increasing the future quantum workforce.

Jobs and roles in quantum computing ecosystem. After analyzing the top 15 companies from the global Quantum Computing Ecosystem (some companies considered are IBM, Amazon, Microsoft, and Google), Draup et al. [8] has identified that typically all relevant job roles can be mapped & structured across 5 unique Job Clusters. See Table 1, which presents examples of jobs, cluster, skills required and workload.

Table 1. . QC job clusters and roles

Job ID	Job Cluster	Skills ID	Workload ID
JB01	Software Engineering	SK01	WL01
JB02	Software Engineering	SK01	WL01
JB03	Software Engineering	SK01	WL01
JB04	Hardware Engineering	SK02	WL02
JB05	Hardware Engineering	SK02	WL02
JB06	Hardware Engineering	SK02	WL02
JB07	Hardware Engineering	SK02	WL02
JB08	Hardware Engineering	SK02	WL02
JB09	Research Science	SK03	WL03
JB10	Research Science	SK03	WL03
JB11	Research Science	SK03	WL03
JB12	Research Science	SK03	WL03
JB13	Research Science	SK03	WL03
JB14	Technical Consulting	SK04	WL04
JB15	Technical Consulting	SK04	WL04
JB16	Technical Consulting	SK04	WL04
JB17	Product & Program Management	SK05	WL05
JB18	Product & Program Management	SK05	WL05
JB19	Product & Program Management	SK05	WL05

JB01: Software Development Engineer – Quantum.

JB02: Embedded Software Engineer.

JB03: Quantum Software Engineer, Test and Measurement.

WL01:

Advancing the entire quantum computing technology stack & full stack architecture.

Exploring applications to make quantum broadly usable and accessible.

SK01: C, C++, Java, Python, Spring, MATLAB, HTML, Simulink, PostgreSQL, Julia, software scripting for hardware interfaces.

JB04: Cryogenic Integration Engineer.

JB05: Design Verification Engineer.

JB06: Signal Integrity Engineer – Quantum.

JB07: Quantum Device Fabrication Engineer.

JB08: Quantum Test Engineer.

WL02:

Solve problems related to the fabrication and characterization of novel quantum processors.

Assemble & test complex electrical/ mechanical systems, cryogenic systems, microwave electronics to develop quantum hardware.

SK02: C, C++, Java, Python, Spring, MATLAB, Hardware Interface Programming, Cryogenic Operations, Device Fabrication (Lithography).

JB09: Quantum Scientist.

JB10: Quantum Data Scientist.

JB11: Quantum Research Scientist.

JB12: Quantum Science Researcher.

JB13: Applications Research Scientist.

WL03:

Responsible for architecting compiler optimizations in the Quantum Information Science Kit (Qiskit).

Thought leadership in quantum algorithms and/or quantum architecture research.

SK03: C, C++, Java, Python, Spring, MATLAB, HTML, Simulink, PowerBI, Tableau, Qlik, Quantum Mechanics, Theoretical Physics.

JB14: Solutions Architect (Quantum).

JB15: Industry Quantum Consultant.

JB16: Quantum Computing Technical Expert.

WL04:

Develop solution reference archt. aligned to business needs & evolving capabilities of emerging tech.

Design technical solutions that take advantage of the Cloud platform & Quantum Computing services.

Provide Consumer, Retail, & Agri-business industry-specific thought leadership & advisory services.

SK04: Python, HPC, ML/DL algorithms, Cloud Computing, SOA, Server-less Architecture, GPUs, Linear Programming, Qiskit, Quantum Consulting.

JB17: Product & Program Management.

JB18: Product & Program Management.

JB19: Product & Program Management.

WL05:

Define and drive an organization-wide strategy for Quantum Computing.

Engage with customers directly to identify new capabilities product features for the use of Quantum Computing to achieve end goals.

SK05: C, C++, R, Python, STATA, SAS, SPSS, Adobe Design, Cloud Services, Product Roadmap, User Stories, Wireframes, UI/UX.

As we can see, these broader jobs require a range of skills listed in the description, however, most of which are not quantum related.

Despite the lack of accuracy in the skills expressed in such job descriptions, there are other efforts on gathering the skills required by quantum job positions, as we can see in the next section.

RELATED WORKS

Being quantum-ready involves a combination of both theoretical knowledge and practical skills needed to work in the rapidly evolving field of quantum technologies [36].

Academic institutions can play an important role in filling the gaps needed to be quantum-ready by providing individuals with the foundational knowledge and transferable skills through specialized academic programs, conducting research, partnering with industry for hands-on training.

Quantum mechanics by nature is complicated due to the physics concepts involved and the mathematical expressions. Derived from this, Quantum Information Science and Technology sounds difficult to learn and teach. Thus far, research on the effectiveness of QIST-related courses, curricula, and pedagogies has been limited in scope [37]. Postsecondary educators have investigated the nature of students’ learning difficulties in quantum courses. Educators have also developed modular QIST learning tools that can be adapted to courses at the undergraduate and graduate levels.

One challenge in teaching QIST is the absence of a common curriculum, in large part because the field is highly interdisciplinary and relatively new [37]. In the last decade, educators across academia and industry reflected on the urgent need for bachelor’s degree programs, courses, and curricular materials for quantum information science and engineering.

Efforts in Quantum Computing Education

In [37], it is argued that an introductory course on quantum computation can easily integrate resources by pairing lecture topics with hands-on activities. It is proposed that hands-on QIST approaches result in deeper understanding and more rapid uptake of quantum concepts, according to a survey conducted after a 2020 remote global summer school hosted by IBM.

The syllabus was based on IBM’s educational activities and interactive materials, including the following parts:

Traditional course structure: Module 1: linear algebra, dirac notation, quantum mechanics; Module 2: quantum algorithms; Module 3: quantum hardware.

Supplementary hands-on materials: Module 1: phyton, qiskit; Module 2: quantum programming; Module 3: quantum hardware calibration, error mitigation, transpiling.

This course is based on the advising of IBM, who recommends supplementing traditional quantum computation course topics with hands-on supplementary materials that incorporate real quantum systems. A more organized view is shown in Table 2.

Table 2. . Quantum computation course topics with hands-on supplementary materials

Traditional course structure	Supplementary hands-on materials
Module 1:
Linear algebra	Phyton
Quantum mechanics	Qiskit
Dirac notation
Module 2:
Quantum algorithms	Quantum programming
Module 3:
Quantum hardware	Quantum hardware calibration
	Error mitigation
	Transpiling

This study reported good results in implementing the course. However, it only represents an initiative, but it cannot be taken as a reproducible case.

In [13], Bungum and Selstø argued that there is a lack of traditions, research, and development on to what extent, and how, information technology students without a background in physics should be taught quantum physics. Key topics are suggested for a course for information technology students on the master’s level. Eight topics in quantum physics and quantum computing are considered.

(1) the wave functions;

(2) the dynamics of a moving wave function;

(3) quantization (time-independent Schrödinger equation);

(4) entanglement;

(5) specific quantum algorithms;

(6) universal gates and approximations thereof;

(7) quantum solutions to optimization problems;

(8) noisy intermediate scale quantum computing.

By means of group interviews and questionnaires, the students’ experiences of the course are investigated. Results indicate that information technology students are capable and interested in learning quantum physics for the purpose of education in quantum computing. An integrated approach, where students learn quantum physics and quantum computing in the same course, is found to work well for most students. However, as the challenge is extensive for some, it is important to make the purpose of each component of the content clear.

In [38] German et al., expressed the motivation on the fact that QIST is inherently interdisciplinary and spans physics, computer science, mathematics, engineering, chemistry, and materials science. Based on this, they presented three curricular plans for incorporating QIST topics (via quantum computing) into the computer science undergraduate curriculum. Such plans have been constructed with a preliminary consultation with QED-C members (industry, academia, national labs, and government agencies) asking for comments, suggestions, and general input on these three curricular plans.

A list of topics was integrated for a one-semester class that could be extended to a two-semester sequence if supported by an adequate number of lab sessions, which are the following:

The Wave-Particle Duality Principle.

The Uncertainty Principle in the Double-Slit Experiment.

Qubits, superposition, measurement, photons as qubits.

Basic probability, trigonometry, simple vector spaces.

Supporting formalisms: complex numbers, Euler’s formula.

Systems of two qubits. Entanglement. Bell states.

The No-Signaling theorem.

Axioms of QM: the superposition principle, the measurement axiom, and the unitary evolution of quantum states.

Single qubit gates: X, Z, H, etc.

Two qubit gates and tensor products. Working with matrices.

The No-Cloning Theorem.

The Quantum Teleportation Protocol.

Early quantum algorithms: Deutsch-Jozsa, Bernstein-Vazirani.

Simon’s algorithm (as a precursor to Shor’s algorithm)

Deutsch–Jozsa with Mach–Zehnder Interferometers.

Quantum Factoring (Shor’s Algorithm)

Quantum Search (Grover’s Algorithm)

Physical implementation of qubits.

The nine qubit modalities currently in use.

Classical control of a Quantum Processing Unit (QPU)

Error mitigation and control. NISQ and beyond.

Postquantum encryption

Quantum Key Distribution (QKD).

The Quantum Internet.

Adiabatic Quantum Computation (AQC)

Quantum Annealing (QA)

Also, German et al. proposed learning outcomes, based on this list of topics, at the end of the course we would want students to understand that:

(1) A quantum object (a) is produced as a particle, (b) propagates like a wave, and (c) is detected as a particle with a probability distribution that corresponds to a wave.

(2) At the quantum level nature is inherently probabilistic.

(3) Entanglement can be used to create non-classical correlations, but there is no way to use quantum entanglement to send messages faster than the speed of light.

(4) Nature is inconsistent with any local hidden variable theory.

(5) Quantum gates implement time evolution of a quantum state.

The students should become aware of the following:

(1) The power and idiosyncrasies of quantum communication.

(2) The power of quantum parallelism and the role of constructive vs destructive interference in quantum algorithms given the probabilistic nature of measurement(s).

And students should understand that:

(1) Quantum computation breaks the extended Church-Turing thesis but does not violate the original Church-Turing thesis and what the difference is.

(2) Quantum computation already occurs in nature. We are just trying to get better at harnessing it.

Efforts in Quantum Software Engineering Education

Some work has been done on analyzing the impact of quantum computing on software engineering. Some studies have analyzed the implications of quantum computing on each phase of software development lifecycle, as well as the progress in developing quantum adaptation to each phase.

An example of this effort is presented in [23], where the required technical competencies that master students of computer science should have in quantum computing were identified. In addition, it also analyzes the current state, i.e., the technical competencies that graduates of the bachelor’s program in computer science have in relation to SE for QC.

Kiefl and Hagel presented an analysis of the characteristics of the software development process for classical SE and for QC SE. These phases were described:

requirements phase;

design phase;

implementation phase;

test phase;

installation and checkout phase.

Each phase was analyzed and characterized in terms of the nature of the activities for each phase, emphasizing the quantum concepts involved in the QC approach of SE.

With a structured competence analysis, the competences are collected, documented, and compared. It shows that the current state (of the level of competence) does not correspond to the required target state and that further technical competencies are required. Furthermore, it is proposed that related topics such as mathematics, physics, complexity theory, etc., must also be considered and investigated, and being included in the curricula design guidelines, how it is done, for example in the SWEBOK [39] for all the software development phases. Based on this work, a teaching concept should be developed which implements the results of the competence analysis.

This conclusion evidences the necessity to continue working on the specification of quantum topics that support the software development phases and preparation of students according to those quantum topics.

In [40], Gatti and Sotelo present their experience of a quantum computer course addressed for the first time for undergraduate engineering students. In this study, students’ levels varied from year two to five of their careers and had previous knowledge on calculus, linear algebra and programming, but not on quantum mechanics or on modern physics.

The main objective of the course was that students acquire programming skills in quantum computing, so it had a practical approach. Instead of beginning by introducing the physical phenomenology under the field, the course started directly with presenting the logic of quantum computing from an abstract point of view. The language used was Q#.

The curricula were based on the one available for the Microsoft Quantum Network:

Topic 1 – Introduction to quantum computing.

1.1. The qubit vs. the bit. Bloch sphere, overlap, measure.

1.2. Systems of several qubits, tensor product, entanglement, measure.

1.3. No-cloning theorem.

1.4. Evolution of systems, quantum gates. Review of normal matrices and their spectral decomposition.

1.5. Introduction to Q#. Implementation of states and gates.

Topic 2 – Simple algorithms.

2.1. Representation of quantum circuits

2.2. Teleportation

2.3. Deutsch algorithm

2.4. Extension to the Deutsch-Jozsa algorithm

Topic 3 – QFT, Simon, Phase, and Shor algorithm.

3.1 Implementation of the quantum Fourier transform for two qubits.

3.2 Implementation of the general quantum Fourier transform.

3.3 Simon’s algorithm and phase estimation.

3.4 Shor factorization algorithm, relationship with the RSA system of classical cryptography.

Topic 4 – Grover’s algorithm.

4.1 Introduction to algorithms by oracles.

4.2. Rotation in the solution spaces of a search in unstructured data.

4.3. Implementation of the algorithm.

4.4. Optimality of search steps.

Topic 5 – The reality of quantum computers.

5.1. Physical implementations of the qubit.

5.2. Limitations.

5.3. Industry and associated business areas.

After completing the course, some conclusions were stated:

(1) Engineering students from year 2 to 5 of their careers were able to properly pass the course, acquiring practical skills in programming quantum computers.

(2) Students in the initial stage of their careers after pursuing algebra and calculus can take more profit of an introductory course on quantum computing, even awaking research vocations, than those in more advanced stages, which are more oriented to technologies currently in use in the industry.

(3) Students approach this field moved by curiosity and a certain halo of mysticism that surrounds the subject. This imaginary of a quasi-magical functioning collapses when faced with mathematical formulation, strongly discouraging many of the naive curious. The main challenge was to show, even in the most basic formulations, the advantages offered by this theory over classical computing.

(4) In this kind of course, it is essential to explain in depth simple algorithms such as Deutsch–Jozsa or Grover’s since this allows the students to understand the power of quantum computing.

Improving Software Engineering Activities through Quantum Algorithms

In [41], an especial motivation was addressed: quantum computers (QCs) are maturing; when QCs are powerful enough, they may be able to handle problems in chemistry, physics, and finance that are not classically solvable. However, the applicability of quantum algorithms to speed up software engineering tasks has not been explored.

Miranskyy et al. [41] examined eight groups of quantum algorithms that may accelerate SE tasks across the different phases of SE and sketch potential opportunities and challenges:

(1) Systems of sparse linear equations solvers. Systems of linear equations can be used to solve some SE problems.

(2) Eigenvalue solvers. An eigenvalue solver is used to find the eigenvalue of an eigenvector. Eigenvalues and eigenvectors can be used to assess the importance (centrality) of developers and code modules to predict code quality. They may also be used to identify high-risk software.

(3) Systems of differential equations solvers. Many SE problems can be modelled using systems of linear and non-linear differential equations. They can, for instance, assist in the development of self-adaptive software systems [42, 43] and assessing project risks associated with changing requirements.

(4) Data fitting. The least squares method is often helpful for fitting data in various SE areas, such as cost estimation, software reliability forecasting, and defect prediction.

(5) Quantum machine learning (QML). Machine learning can be used to support most SE activities, from requirements engineering to maintenance [44]. Liu et al. [45] demonstrated how QC could be used to perform classification using the heuristic quantum kernel method resulting in exponential performance gains over classical algorithms. Thus, QML algorithms can be created for QC to process regular datasets efficiently.

(6) Combinatorial optimization. Combinatorial optimization techniques, such as integer programming and mixed integer programming (MIP), are essential in SE from release planning and requirements prioritization to test case prioritization [46] to selecting an optimal set of customers to profile. A quantum approximate optimization algorithm and its extensions (e.g., [47], [48]) have been proposed for gate-based noisy intermediate-scale quantum (NISQ) devices.

7) Search or string comparison. String comparison and pattern matching are omnipresent in SE, appearing in areas of static and dynamic analysis, such as test selection and generation, code coverage inspection [49], log or trace analysis [50], and cybersecurity [51], [52].

8) Boolean satisfiability solvers. Many SE use cases (e.g., static analysis software model checking, false path pruning, and test suite reduction) can be formulated as a Boolean satisfiability (SAT) problem with many literals푘. QCs show promise at solving SAT problems.

These techniques appear throughout the software development lifecycle, from requirements engineering to maintenance, as good supporting tools to improve software creation. However, Miranskyy et at. emphasize that the community can develop the algorithms and software foundation in time for the hardware to arrive.

The findings of [41] suggest that software engineers must be capable of implementing and using such level of algorithms. To do this, it is needed to manage quantum computing fundamentals.

Classifying Quantum Computing Workforce

In [40], Gatti and Sotelo synthesize the classification of workforce in six categories, proposed by [53]. See Table 3.

Table 3. . Classification of quantum workforce

Category	Description
Quantum curious	Individuals who are just asking the very basic about QC
Quantum explorer	People who start exploring some concepts of QC
Quantum climber	People who decide to get educated about QC
Quantum enabled	Individuals familiar with the syntax of QC languages and platforms
Quantum ready	People who understand and can write quantum circuits and understand complex algorithms
Quantum professional	Individual with knowledge and skills to reach the market

This classification is supported by [54], where Plunkett at al. presented a survey report which identifies current approaches to educate students from varied learning groups, including professionals looking to increase their skillsets, high school students exploring their interests, and individuals seeking a formal master’s degree in the field.

The classification shown in Table 3 allow us to: (1) visualize the different levels of qualification to engage in quantum computing, into which practitioners can be ranked; (2) design courses and practices on quantum computing pretending one of these levels, this can be done in combination with the other proposals of proficiency levels such as [55] and guidelines based on the traditional Bloom taxonomy [56, 57].

METHODOLOGY

In this section we describe the methodology used to perform the literature review. To perform this review, we considered the recommendations for systematic mappings (SM) from [58–60]. Also, we considered recommendations for systematic literature reviews (SLR) from [61–66], especially for establishing selection criteria. Both methods are complimentary, in terms of strategies for conducting the review and for complementing the scope of the search.

Sometimes additional sources are well accepted to enrich the coverture of the review [65], including manual and less structured searches of the Internet and other sources [67] and grey literature as is recommended in [68].

In an unstructured search we identified other work (not included in the formal search) with significant contribution, so we decided to review these references. Also, we considered additional sources referenced in the selected papers, which were indicated as containing fundamental concepts of quantum computing and proposals for quantum computing curricula. So that, the results include references from formal search and additional sources.

The capacity of SM enables us to perform this literature review because the objective of this search is only to locate the skills required for quantum computing and software engineering, relating the fundamental concepts of quantum computing and quantum software engineering, without making a deep analysis of the state of the art of each subject or of the solutions given to problems presented or challenges faced by these disciplines. In general terms, we are looking to identify the competences that practitioners should have to work on quantum computing and developing quantum software.

Next, we are going to describe the process for the review in terms of systematic mapping.

Definition of Research Questions (Outcome: Research Scope). Software is an important element for computation [30]. Quantum software applications are getting popular because the power of quantum computing facilitates applying this paradigm to solve complex problems in any field of science and the real world [32], [69]– [71]. Quantum software plays a critical role in exploiting the full potential of quantum computing systems [28]. Quantum applications require the use of a completely different kind of computer and algorithms, which have the potential to solve tasks that we do not even dare dream of today [31], [72]. Considering the significance of software in the quantum world and the required skills to produce quantum software, we state the main objective of the literature review.

Objective of literature review: To look for the skills required in quantum industry to possess by workforce to implement quantum computing, and specially to develop quantum software. Furthermore, we intend to precise the quantum knowledge involved and to recognize both technical (hard) and soft skills required.

It is important to remark that in a previous study [73] a first proposal of fundamental concepts involved in quantum computing is presented. In the current study, the set of fundamental concepts is increased.

Research questions: Three main research questions were formulated, which are the following:

RQ1: What is the knowledge that quantum computing workforce should have?

RQ2: What are the hard skills that quantum computing workforce should have?

RQ3: What are the soft skills that quantum computing workforce should have?

Searching phrases: We decided to formulate a search phrase which includes the topics of quantum computing, software, and skills. We hope to reach for such papers which emphasize the skills required for quantum software development and establishing a relationship with quantum computing because it provides the fundamental elements for quantum software. The searching phrase is the following:

(“quantum computing”) AND (“software engineer” OR “software developer” OR programmer) AND (skills OR competences)

Databases considered: Four databases were considered, ACM, IEEE Xplore, Scopus, and ScienceDirect.

Period: Sources were considered until June 2023, when the search was done.

Developing review protocol: In a session with the participation of two researchers, we defined a kind of general protocol, considering the following aspects:

– What type/source of papers to consider.

– What parts of the papers should be revised.

– How many reviewers are going to review the same set of papers.

– Defining the filters for selecting the papers.

– Formats for gathering information.

Conduct Search for Primary Studies (Outcome: All Papers)

Identifying the relevant research: A user account from a Mexican institution was utilized, with the proper privileges to access to the advanced search section on the website of databases and obtaining the corresponding source files of the papers.

The result of the search is shown in Table 4. The four databases provide more than 400 items from the search phrase.

Table 4. . Databases consulted

Database	Number of papers (items) found
ACM (AC)	232
ScienceDirect (SD)	105
Scopus (SC)	69
IEEE Xplore (XP)	32

Screening of Papers for Inclusion and Exclusion (Outcome: Relevant Papers)

Selecting the primary studies: We defined a structure for identifying the resulting documents: demographic aspects, inclusion criteria, and exclusion criteria.

Demographics: This attribute identifies the nature of the document.

D1: Type of document (Research paper, communication paper, white paper). We decided to select research papers, unless there may be other types of work with significant contributions.

D2: Origin of document (Conference, Journal, Book, other.) We decided to select papers from journals and conferences, unless there may be other types of work with significant contribution.

D3: Language – (Results that are written in English/Spanish). We decided to consider only work written in English.

D4: Accessibility – Full texts are accessible by means of the institutional accounts.

Inclusion criteria: We established inclusion criteria on two levels, in the form of filters.

Level 1: Header of the paper

F1: Title of the paper, it contains: One significant word of a phrase (e.g., quantum, software engineer, skills), one part of the searching phrase, or two parts.

F2: Keyword section, it contains: One significant word of a phrase (e.g., quantum, software engineer, skills), one part of the searching phrase, or two parts.

F3: Abstract section, it contains a stablished relationship between “quantum computing” and “software engineer” and “skills,” for example:

– There are concepts related to one or both areas (“quantum computing,” “software engineer skills”), explicitly cited.

– A relationship between “quantum computing,” “software engineer,” “skills” is established. For example: “QC is implemented, in part, based on software, that is, software is an important element of QC; and the skills required are mentioned”; “quantum software includes fundamental concepts of quantum mechanics, software engineer should have skills to produce such software”; “there is a dependency between QC and software, and specific skills are required”; and so on.

Note: F3 was the filter with the highest acceptance value elements. We noticed that in some cases, the title and keywords section did not contain the expected elements, however, the abstract gave signs that the paper contains contribution. In some items, the body of the paper contains the elements we are looking for, so this section becomes the main acceptance value.

Level 2: Body of the paper

B1: Results that introduce and describe concepts of QC and/or quantum software and the required skills to implement them.

B2: Results that discuss Quantum Computing and some aspects of quantum software, or vice versa, citing required skills.

Exclusion criteria: Exclusion criteria are oriented to removing items that we consider don’t provide relevant information to the research or not containing complete information, or not availability.

EX01: Remove the duplicates found in the sources. (A very low percentage was found).

EX02: Remove items that are not research papers. (Unless there may be other types of work with significant contribution.)

EX03: Remove papers if only the abstract but not the full text is available.

EX04: Remove results not written in English. (None was found).

EX05: Results that do not introduce and describe the concepts of quantum computing and/or quantum software engineering.

EX06: Results that do not discuss the association between computing and/or quantum software, software engineer, and skills.

Results of selection: We applied the exclusion criteria EX01, EX02, EX03, and EX04, as well as the filters of level 1, having the selection expressed in Table 5. In Appendix A, the papers are labeled with consecutive numbered notation as S1, S2, …Sn. Appendix A contains the complete list of the papers, Table 9.

Table 5. . Databases consulted

Database	Number of papers (items) found
ACM (AC)	37
ScienceDirect (SD)	6
Scopus (SC)	5
IEEE Xplore (XP)	3

As we mentioned earlier, we considered all the papers in this selection stage, trying to consider a wider spectrum of literature to detect the fundamental concepts. Furthermore, we include additional sources to complete the study (these items are cited in the reference list).

Keywording of abstracts (outcome: classification scheme)

According to the objective of the research, we created four categories for classifying the selected papers:

(1) Industry’s skills requirements focus (Category 1).

(2) Education/curriculum -QC and SE skills cultivation (Category 2).

(3) Requirements of skills for QC, in general (Category 3).

Category 1: This category refers to the requirements of the workforce from industry, in general terms or for software development.

Category 2: This category refers to the efforts of developing skills for quantum computing and software development, a connection between both areas.

Category 3: This category refers to the manifestation of skills required for quantum computing in general terms, that is, it emphasizes the nature of quantum computing and the derived skills needed for quantum compunting.

Data Extraction and Mapping of Studies (Outcome: Systematic Map)

In Table 6 the grouping of papers is presented in terms of the three categories indicated. As we can see, Category 2 has the highest frequency of papers, followed by Category 3, and Category 1 is close to Category 3. The results show that the academy is worried about preparing skilled graduates and working on it to meet the requirements from industry and the imposed challenges of quantum computing.

Table 6. . Grouping papers into categories

Category (focus)	References
1. Industry’s skills requirements focus	S13, S18, S22, S24, S26, S41, S42, S43, S44, S45, S50
2. Education/curriculum (QC and SE skills cultivation)	S1, S4, S8, S10, S11, S12, S13, S14, S17, S19, S20, S21, S23, S25, S26, S27, S28, S29, S30, S31, S32, S33, S34, S35, S36, S37, S44, S46, S49, S51
3. Requirements of skills for QC, in general	S2, S3, S5, S6, S7, S9, S15, S16, S18, S38, S39, S40, S45, S47

The results from the analysis of the mapping are presented in the next section, answering the research questions.

RESULTS

To describe the results, we consider that competence involves knowledge, behaviors, attitudes and even skills that lead to the ability to do something successfully or efficiently.

A skill, on the other hand, is learned and involves applied abilities that use one’s knowledge effectively in execution or performance. Skills are the components that go into building competence. Next, we describe the three main components of competence, knowledge, hard skills, and soft skills, through the research questions.

RQ1: What is the knowledge that quantum computing workforce should have?

To answer this question, we considered spread quantum concepts cited in the sources consulted from Table 6. However, to have a complete understanding of the main concepts, some definitions presented in this section were gathered from supporting literature. As basis, we consider the fundamental concepts of quantum computing proposed in [74].

A taxonomic view is described including the main knowledge. This allows us to have a complete and more comprehensive framework of knowledge.

Quantum information theory (QIT). A significant set of knowledge is encompassed in this discipline. QIT is the study of the achievable limits of information processing within quantum mechanics [75]. Many different types of information can be accommodated within quantum mechanics, including classical information, coherent quantum information, and entanglement. Exploring the rich variety of capabilities allowed by these types of information is the subject of quantum information theory.

QIT is an interdisciplinary field that involves quantum mechanics, computer science, information theory, philosophy, and cryptography among other fields. Electronics is a closely related discipline. See Fig. 1, where QIT is referred to as Quantum Information Science.

Fig. 1. [Images not available. See PDF.]

Quantum information science–interdisciplinary composition.

Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory [76] and can be manipulated using quantum information processing techniques. Quantum information refers to both the technical definition in terms of von Neumann entropy and the general computational term.

Information theory. Information theory is the mathematical study of the quantification, storage, and communication of information [77]. The field is at the intersection of probability theory, statistics, applied mathematics, computer science, statistical mechanics, information engineering, and electrical engineering. See Fig. 2.

Fig. 2. [Images not available. See PDF.]

Information theory–interdisciplinary intersection.

Important subfields of information theory include source coding, algorithmic complexity theory, algorithmic information theory and information-theoretic security. See Fig. 3.

Fig. 3. [Images not available. See PDF.]

Information theory–subfields.

Quantum mechanics. Quantum mechanics is the area of physics that studies the behavior of particles at a microscopic level [78, 79]. At subatomic levels, the equations that describe particles behavior are different from those that describe the macroscopic world around us. Quantum computers take advantage of these behaviors to perform computations in a completely new way. The main concepts of quantum mechanics are shown in Fig. 4.

Fig. 4. [Images not available. See PDF.]

Quantum mechanics–fundamental concepts.

Well-described definitions of quantum mechanics fundamentals are presented in [79–81], and well explained in [82], such as superposition, entanglement, and decoherence, as well as the qubit as the fundamental unit of computation.

A more detailed description of quantum mechanics is shown in Fig. 9 (See APPENDIX C). In this view, some fundamental concepts are described in terms of specific concepts.

Mathematics. Mathematics as a field is apporting to quantum computing through two subfields, probability for measuring quantum states, and linear algebra for matrix representation of quantum gates, which are mechanisms to perform quantum computation. A detailed view of mathematical concepts involved in quantum mechanics is shown in .

Fig. 5. [Images not available. See PDF.]

Mathematics–detailed list of concepts for quantum computing.

Fig. 6. [Images not available. See PDF.]

Computer Science – specific topics.

Fig. 7. [Images not available. See PDF.]

Cross-disciplinary teamwork of quantum computing practitioners.

Fig. 8. [Images not available. See PDF.]

Scale for assessing competences.

Fig. 9. [Images not available. See PDF.]

Quantum mechanics–a detailed view.

Physics. Physics is the basic science that encompasses quantum mechanics [83], [84], so it is important to consider some fundamental concepts of this science. In [85]–[87] the contribution of physics to quantum computing is emphasized. Figure 10 shows a list of topics to consider (See APPENDIX C).

Fig. 10. [Images not available. See PDF.]

Physics–detailed view of fundamental concepts converging to quantum mechanics.

Computer Science. Computer science is the study of computation, information, and automation [88]– [90]. Computer science spans theoretical disciplines (such as algorithms, theory of computation, and information theory) to applied disciplines (including the design and implementation of hardware and software). See Fig. 11 (See APPENDIX C). Computer science provides significant concepts and principles to quantum computing [10].

Fig. 11. [Images not available. See PDF.]

Computer science–detailed view of subfields and related disciplines.

Quantum computing has a strong relationship with computer science because computation is performed by a computer. The idea of Feynman to implement quantum computing gives the strong relationship between the concepts of quantum mechanics and computer science.

Specific topics that could be related to quantum computing are shown in Fig. 6.

RQ2: What are the hard skills that quantum computing workforce should have?

Hard skills, also called technical skills, are any skills relating to a specific task or situation. It involves both understanding and proficiency in such specific activity that involves methods, processes, procedures, or techniques [91].

Technical skills are closely related to knowledge, to that, the answer of RQ1 provides a knowledge framework for technical skills.

Also, to answer this question, we considered spread technical skills cited in the consulted sources from Table 6. However, better integrated proposals were gathered from supporting literature.

In [92] a proposal of skills required in quantum industry is presented, divided into groups for recommended courses. Fox et al. [92] designed an interview, it was semi-structured, meaning that deviations from the script were allowed for clarification of statements from the interviewee.

The lists of scientific and technical skills used as prompts in the interview protocol were taken from the 2016 report of the Joint Task Force on Undergraduate Physics Programs [87]. This supporting work emphasizes knowledge and scientific and technical skills, describing them as follows.

Physics-specific knowledge: Learning goals for physics-specific knowledge include the ability to use fundamental concepts such as conservation laws to solve problems, and competency in applying basic laws of physics in diverse topic areas and applied contexts. They also include the abilities to represent physics concepts in multiple ways and solve problems involving multiple topic areas and disciplines.

Scientific and technical skills: Learning goals for scientific and technical skills include the abilities to solve ill-posed problems through experiments, simulations, and analytical models; determine follow-on investigations; and identify resource needs. They also include competencies in instrumentation, software, coding, and data analytics.

To perform the study, companies from the U.S. engaged in activities that fall within the quantum industry were contacted through the QED-C (approximately 70 companies at that time) on September 22, 2019. Specifically, people who were involved with the hiring and supervision of new employees were asked to contribute to the study. The companies were provided with anonymity. A sample of 21 companies were interviewed. The main activities of the companies were: sensors, networking and communications, computing hardware, algorithms, and applications, and facilitating technology.

We are taking this set of technical skills (hard skills) as the basis for the mapping. Table 7 contains a synthetic view of four categories of skills. Table 8.

Table 7. . Classification of skills for quantum workforce

Category	Skills
Skills real-world quantum information theory	Coding; Statistics and data analysis; Troubleshooting (debugging); Noise sources; Modeling; (De)coherence; Error correction; Open system dynamics; Qubit hardware; Hamiltonians; Quantum circuit design (physical).
Skills of relevance to the quantum industry for a possible traditional quantum theory course	Linear Algebra; Statistics (related to measurement); Unitary time evolution Schrödinger’s equation Hamiltonians; Hilbert space; Entanglement; Two-level systems; Spectroscopy; Atomics energy levels & photon interaction.
Skills of relevance to the quantum industry for a possible quantum information theory course	Linear Algebra; Statistics (related to measurement); Noise sources; Quantum circuit design and gate model; Algorithms; Qubit-abstract; Complexity theory; Quantum secure communication; Hamiltonians; High performance computing.
Skills of relevance to the quantum industry for a possible hardware for quantum information course	Software; Coding; Laboratory skills and experience; Troubleshooting; Materials; Cold atoms; Ion trapping; Laser cooling; Magneto-optical trapping; Bose-Einstein condensates; Superconducting circuits; Photonic integrated circuits; High performance computing; Annealing.

Table 8. . Main soft skills required for the quantum computing industry

Soft skill	SM reference
Analytical/critical/creative thinking	S3, S20, S22, S23, S33, S34
Attitude	S20, S22, S26, S34, S42
Time management	S22, S33, S34, [87]
Teamwork	S22, S33, S34, [87]
Oral/written communication	S22, S33, S34, [87]
Active learning/curiosity	S22, S34, [87]
Ability of self-manage but knowing when to ask for help	S22, S33, S34, [87]
Ability to work across multiple disciplines	S22, S33, S34, [87]
Coping with ambiguity	S22, S23, S42
Leadership and social influence	S22, S23, S33, S34

Table 9. . Selected papers after applying all the inclusion and exclusion criteria -systematic mapping.

ID_DB	ID_TR	Ref.	Paper title
ACM:
AC-2	S1	[97]	Teaching Quantum Computing through a Practical Software-driven Approach: Experience Report
AC-3	S2	[3]	Quantum Computing: A New Software Engineering Golden Age
AC-4	S3	[33]	Towards Higher-Level Abstractions for Quantum Computing
AC-5	S4	[34]	Quantum Software: Model-driven or Search-driven? A Q-SE 2021 Workshop Report
AC-6	S5	[1]	Quantum computing: challenges and opportunities
AC-7	S6	[25]	Bugs in Quantum computing platforms: an empirical study
AC-8	S7	[26]	Making Quantum Computing Open: Lessons from Open Source Projects
AC-9	S8	[23]	Software Engineering Education of Classical Computing vs. Quantum Computing: A Competency-Centric Approach
AC-10	S9	[98]	The business of quantum computing
AC-12	S10	[99]	Quantum Computing As a Topic in Computer Science Education
AC-15	S11	[100]	First International Workshop on Quantum Software Engineering (Q-SE 2020)
AC-18	S12	[101]	Entanglion: A Board Game for Teaching the Principles of Quantum Computing
AC-20	S13	[102]	QAI4ASE: Quantum artificial intelligence for automotive software engineering
AC-21	S14	[103]	Hybrid quantum-classical problem solving in the NISQ era
AC-22	S15	[104]	Thinking Too Classically: Research Topics in Human-Quantum Computer Interaction
AC-23	S16	[105]	Building a quantum computer
AC-25	S17	[106]	Exploring Quantum Reversibility with Young Learners
AC-26	S18	[107]	The Holy Grail of Quantum Artificial Intelligence: Major Challenges in Accelerating the Machine Learning Pipeline
AC-27	S19	[108]	Cyberinfrastructure Facilitation Skills Training via the Virtual Residency Program
AC-31	S20	[109]	Reflections on cyberethics education for millennial software engineers
AC-32	S21	[110]	Qupcakery: A Puzzle Game that Introduces Quantum Gates to Young Learners
AC-39	S22	[111]	65 competencies: which ones should your data analytics experts have?
AC-40	S23	[112]	Interactive online tool as an instrument for learning mathematics through programming techniques, aimed at high school students
AC-41	S24	[113]	Evolution of the Competencies to Embrace Digital Technology for Sustainable Development
AC-46	S25	[114]	A golden age for computing frontiers, a dark age for computing education?
AC-47	S26	[115]	Beyond the badge: reproducibility engineering as a lifetime skill
AC-48	S27	[116]	To Write Code: The Cultural Fabrication of Programming Notation and Practice
AC-49	S28	[117]	Should Quantum Processor Design be Considered a Topic in Computer Architecture Education?
AC-50	S29	[38]	On the Design and Implementation of a Quantum Architectures Knowledge Unit for a CS Curriculum
AC-55	S30	[118]	CT 2.0
AC-56	S31	[119]	The Evolving e-Governance Curriculum: A Worldwide mapping of Education Programs
AC-58	S32	[120]	Positive and negative learning by IT professionals
AC-59	S33	[121]	Exploring Creativity and Learning through the Construction of (Non-Digital) Board Games in HCI Courses
AC-60	S34	[122]	ACM Computer Science Curricular Guidance for Associate-Degree Transfer Programs with Infused Cybersecurity
AC-63	S35	[123]	PESTLE Analysis of Cybersecurity Education
AC-64	S36	[124]	Cultivating the Cyberinfrastructure Workforce via an Intermediate/Advanced Virtual Residency Workshop
AC-35	S37	[125]	High Performance Computing Education: Current Challenges and Future Directions
IEEE Xplore:
XP-7	S38	[126]	Statistical Assertions for Validating Patterns and Finding Bugs in Quantum Programs
XP-12	S39	[127]	A Software Development Kit and Translation Layer for Executing Intel 8080 Assembler on a Quantum Computer
XP-13	S40	[128]	Need and Challenges in Quantum Computing in Fog Environment
Scopus:
SC-7	S41	[129]	Quantum Programming on Azure Quantum—An Open Source Tool for Quantum Developers
SC-21	S42	[130]	Society 5.0 and the future of work skills for software engineers and developers
SC-24	S43	[131]	Industry quantum computing applications
SC-52	S44	[132]	New Programming Paradigms.
SC-57	S45	[133]	Introducing Microsoft Quantum Computing for Developers: Using the Quantum Development K it and Q#
ScienceDirect:
SD-4	S46	[134]	Reigniting the power of artificial intelligence in education sector for the educators and students competence.
SD-6	S47	[135]	QuantuMoonLight: A low-code platform to experiment with quantum machine learning
SD-20	S48	[136]	Industry 4.0 in Terms of Industrial Relations and Its Impacts on Labour Life
SD-26	S49	[137]	The future of sustainable digital infrastructures: A landscape of solutions, adoption factors, impediments, open problems, and scenarios
SD-33	S50	[138]	Industry 4.0 in a project context: Introducing 3D printing in construction projects
SD-55	S51	[139]	Fresh Outlook on Numerical Methods for Geodynamics. Part 2: Big Data, HPC, Education

In APPENDIX B there is a description of the proficiency to be shown by practitioners for each category of skills, also it is indicated the literature attending these skills. Table 10 contains a set of skills required in the real world for affairs related to quantum information theory. Tables 11, 12 and 13 contain sets of skills recommended for specific curriculum courses.

Table 10. . Skills real-world quantum information theory

Skill	Description	Supporting References
Coding	• Be able to program based on established algorithms. • Be able to debug the quantum processor. • Be able to collect and analyze data and discuss the results back with the programmer.	S6, S7, S8, S15, S23, S26, S27, S39, S45
Statistics and data analysis	Be able to refine processes and calibrations of the computer, which involves doing a bunch of experiments and understanding the hypothesis has been nullified or proven.	S23, S29
Troubleshooting (debugging)	Be able to perform a totally different debugging from classical code, because in classical codes programmer can step through and in quantum codes programmer cannot do that because a measurement will be done and when it is done, it just through the information.	S15, S41, S45
Noise sources	Be able to manage noise mechanisms: What a gate model machine is, the principles on how it operates, decoherence and noise mechanics and common failure mechanics for both models of quantum computation.	S16, S51
Modeling	Be able to understand how to take noisy data, understanding what the underlaying physical model of what is dragging that data, knowing how to fit that data and say something statistically meaningful: whether the mode proposed is correct or not, or how to update the model.	S2, S3, S4, S8, S14, S26
(De)coherence	Be able to manage the decoherence mechanism for the technology upon which the sensor operates. It is important to know for a particular application whether you want a system that has a longer coherence time or a system that can easily be coupled to some other system. What are the limits of that kind of coupling?	S9, S10, S11, S12, S16, S17, S28, S29
Error correction	Be able to manage quantum error correction: for quantum error correction, and device design, and simulation obviously need lots of physics.	S11, S12, S16, S17
Open system dynamics	Be able to understand and manage the open system dynamics: The Schrodinger equation drives the time evolution that see or, hopefully even more than unitary dynamics, understanding open system dynamics.	S4, S7
Qubit hardware	Be able to understand qubit behavior, specially how it is going to propagate up in terms of decoherence mechanisms.	S14, S16, S45
Hamiltonians	Be able to apply Hamiltonians capacities: that sort of connection from abstract Hamiltonian to actual physical reality is of course tenuous and needs to be carefully understood what the limits are.	S4, S43
Quantum circuit design (physical)	Be able to design quantum circuits: taking a specification of a quantum system in terms of a Hamiltonian and then turning that into a design that will be fabricated. And there is a lot of microwave engineering there, but also strong connections to quantizing microwave circuits.	S3, S14, S16

Table 11. . Skills of relevance to the quantum industry for a possible traditional quantum theory course

Skill	Description	Supporting references
Linear algebra	Be able to use/apply linear algebra at the level of abstraction required for quantum theory. So abstract vector spaces, abstract operators, complex vector spaces	S23, S29
Statistics (related to measurement)	Be able to manage statics for measurement: Statistical nature of making measurements with photon on atoms	S7, S23, S29
Unitary time evolution Schrödinger’s equation Hamiltonians	Be able to manage unitary time evolution: The Schrödinger equation drives the time evolution. Having enough mathematical understanding of Hamiltonians and time evolution	S4, S7, S43
Hilbert space	Be able to manage the Hilbert space: There is certain basic background that almost everyone on the team really should know, which kind of has to do with the basic formalism of quantum mechanics: Hilbert space and unitary time evolution and measurements and entanglement	S4, S7, S43
Entanglement	Be able to manage entanglement as one of the most significant	S4, S7, S9, S10, S11, S12, S16, S17, S43, S47
Two-level systems	Be able to write down a two-level or three-level system and talk about rate equations for optical pumping and depletion	S4, S7, S43
Spectroscopy	Be able to have a useful conversation about atomic spectra or be able to say like that would not work because the transition’s forbidden because of selection rules	S4, S7, S43
Atomics energy levels & photon interaction	Be able to understand and manage atomics energy levels & photon interaction: atomic physics knowledge so they can do level like level calculations, and modeling, and Franck–Condon factors	S4, S7, S43

Table 12. . Skills of relevance to the quantum industry for a possible quantum information theory course

Skill	Description	Supporting references
Linear algebra	Be able to apply linear algebra for explaining quantum phenomena and operators for qubits treatment. Professionals or practitioners should be able to do the linear algebra, the matrix manipulation, to show what a quantum circuit does	S4, S7, S23, S29, S43
Statistics (related to measurement)	Be able to apply statics for expressing quantum phenomena. Quantum mechanics is the generalized instance of classical probability theory. Sampling from richer probability system	S7, S23, S29
Noise sources	Be able to try with noisy system. It really is just quantum circuits and gates and noise models	S11, S12, S16, S17, S51
Quantum circuit design and gate model	• Be able to understand and design circuits (free of noise) and gate models. Full noise modeling, gate modeling, algorithm optimization, need to be differentiated, because not all gates are the same. And so, the theorists are developing new ways to mitigate noise   • Be able to apply properly and correctly each type of gate: Not necessarily have on call, like what the matrices are for like a CNOT gate and like the Hadamard stuff but be able to show like this is what the system is doing and that at the end of the day, all these evolutions break down into just a matrix multiplication, a bunch of Pauli matrices	S3, S14, S16
Algorithms	• Be able to create and manipulate quantum algorithms. A practitioner must be able to understand the data model and how to translate it into some algorithm that might be used for a specific problem   • Practitioners don’t have to memorize all the algorithms in the zoo, but they need to know which algorithms might want to try with   • Practitioners must be able to figure out a quantum algorithm (than use a quantum programming language), and whether or not we can solve a problem using a quantum computer	S1, S2, S13, S14, S17, S19, S45, S51
Qubit-abstract	Be able to interpret abstract implementation of qubit: The Bloch sphere is a very useful picture of the state space of a qubit and being very f amiliar with that and using that language, because that kind of language is used all the time across the board	S4, S7, S9, S10, S11, S12, S14, S16, S17, S43, S45, S47
Complexity theory	• Be able to manage complexity theory: Quantum computing rests heavily on a lot of computer science, and theoretical computer science, of that, about complexity theory and order runtimes of algorithms and why this might provide speed up   • Be able to scale beyond classical hardware and that people must have kind of like a notion that say, Shor’s algorithm for unstructured search is order root N instead of order N	S7, S10, S12, S43
Quantum secure communication	Be able to apply quantum algorithms to secure communication: What are the encryption algorithms, what are the signatures, how would you think through implementing some security protocols	S4, S35, S36, S37, S43
Hamiltonians	Be able to apply Hamiltonians in solving problems: We have a certain implementation of a superconducting qubit and there is a Hamiltonian associated with that and some kind of energy landscape. What a Hamiltonian is, how to get the eigenstates	S4, S43
High performance computing	Be able to apply methods and techniques for HPC applications: It is needed to understand the sort of state-of-the-art supercomputing methods that quantum computing is up against and then also for some of the applied work. That is, for example, these quantum inspired methods, those ended up running on high performance computing machinery	S35, S36, S37

Table 13. . Skills of relevance to the quantum industry for a possible hardware for quantum information course

Skill	Description	Supporting references
Software	• Be able to show up and know how to do CAD to design systems     • Be able to model quantum systems in Mathematica or MATLAB or whatever other tool     • Be able to not just write the software itself, but, working in a version control system and working in a shared code base where programmers can leverage all the work that other people have done, and other people can leverage to the others	S3, S4, S8, S26, S41
Coding	• Be able to take something that’s being done and look at: how it can be automated, how can certain things be done better, faster, and easier     • Be able to write programs: In general terms, having basic programming skills is probably a necessity in most roles     • Be able to work with others in programming tasks: Working with other people to write programs. Know how to collaboratively write code with code review, write unit tests.Be able to know data structures and how useful APIs might loke like	S6, S7, S8, S15, S23, S26, S27, S39
Laboratory skills and experience	• Be able to work on experiments and projects. People who have been in a machine shop, they know to use a center drill before they drill a hole. People with previous experience in that kind of environment tend to be able to contribute more, and more quickly, because they know what is hard and they know what is not hard   • Folks who can design an experimental program go and implement it, take the data, understand what the data say, and then decide what the next steps are after that	–
Troubleshooting	Be able to solve problems in the daily activity: A lot of the day-to-day work is fighting software and fighting bugs and figuring out what is going on with the fridge	S15, S41
Materials	Be able to create and manipulate new materials: People that are doing materials and process research to try to figure out how to bring in new materials into those devices, what are good thermal insulators, what are the good thermal conductors, what are the good electrical conductors, what are the relationships between those, what are the heat capacities of various things	S4, S7, S43
Cold atoms	Be able to know about lasers, wavelengths, optical components, control, scattered lights, and measurement techniques	S4, S7, S43
Ion trapping	Be able to understand ion trapping technology. The interplay between the electronics and the ions, the physics of just the ion trapping itself, e.g., Mathieu equations, stability regions	S4, S7, S43
Laser cooling	Be able to understand and apply laser cooling material. Using the light to cool down the atoms, removing systematics or trap them in place. Aligning optics, aligning light into fiber optics, using different detectors, electro-optics, acoustic optics	–
Magneto-optical trapping	Be able to manage magneto-optical trapping materials. Building a MOT and trapping atoms, that experience is more valuable than doing full derivations	S4, S7, S43
Bose–Einstein condensates	Be able to manipulate BEC materials and explain its behavior. If somebody is doing some BEC loading into a trap that detects this and that through some phase shift or whatever they are doing, they need to understand that theory. Also, who do that, can go up to a whiteboard and explain that	S4, S7, S43
Superconducting circuits	Be able to manipulate and understand superconducting circuits. If somebody is focusing on coherent times or something, then he/she will have to pick up a lot of material science and quantum circuits design and understand the nitty gritty details of how a superconducting qubit is fabricated and where the fields are and what matters for coherent couplings	S3, S14, S16
Photonic integrated circuits	Be able to manipulate and understand photonic integrated circuits. In this case, practitioners must be able to know how to construct ring resonators; they know how to work with say AIM photonics, like a foundry	S3, S4, S7, S14, S16, S43
High performance computing	Be able to show expertise in kind of traditional HPC, both because, well nowadays, a lot of engineering is done in computer simulation, and we need to have simulation of projected equipment to design it	S35, S36, S37
Annealing	Be able to know what an annealer is and the principles upon how and which it operates	S4, S7, S43

The description given for each skill is an expression of how practitioners should demonstrate the ability to apply knowledge and skills to perform a job’s task related to quantum computing. This means that for each topic or specific knowledge, a description of the proficiency to be shown by practitioners can be written.

RQ3: What are the soft skills that quantum computing workforce should have?

Quantum information scientists draw on the work of physicists, computer scientists, and mathematicians, as well as materials scientists, chemists, and engineers [18]. Cross-disciplinary teams are applying QIS to new quantum technologies in communications, networking, data security, navigation, and medical diagnostics (see Fig. 7). They are also making headway in developing quantum computing systems that may allow us to tackle challenges previously out of reach, in areas such as cryptography, logistics optimization, and across the natural sciences.

As we can see, apart from knowledge about the quantum paradigm, quantum computing practitioners must have strong soft skills to work in multidisciplinary teams and solve problems collaboratively.

Quantum project managers should manage projects based on detailed knowledge of processes, organization, principles, policies and frameworks, information, culture, ethics and behavior, people, skills, and competencies of team members as well as services, infrastructure and applications associated with quantum software and provided by organizations.

Soft skills are a combination of interpersonal, people skills, social skills, communication skills, character traits, attitudes, career attributes and emotional intelligence quotient (EQ) among others [93]. Based on this definition, we collected the main soft skills cited in the literature consulted. See Table 8.

Soft skills are transverse; professionals from any discipline should possess and exhibit them. For example, in [87], a report for physics programs is presented, emphasizing the skills required from industry. Heron and McNeil distinguished two groups of skills, as follows:

Communication skills: Learning goals for communication skills include the ability to communicate orally and in writing with audiences that have a wide range of backgrounds and needs.

Professional and workplace skills: Learning goals for professional and workplace skills include the abilities to work in diverse teams; obtain knowledge about relevant technology resources; demonstrate familiarity with workplace concepts such as project management, budgeting, quality assessment, and regulatory issues; demonstrate effective management of difficult situations (including classrooms); and demonstrate awareness of career opportunities for physics degree holders and effective practices for job seeking.

In Table 13 we collected literature sources from systematic mapping, which includes the skills. Also, we indicated some supporting sources consulted. As we can see, the most cited skills are the following: Analytical/critical/creative thinking; attitude; and leadership and social influence.

It must be emphasized that all industry leaders spoke about the importance of being able to succeed on team projects and effectively communicate technical ideas to a broad audience [94].

The level of proficiency in soft skills normally is acquired from experience, however, certain levels of proficiency can be acquired from curricula formation. While bachelor’s graduates having professional experience may be crucial for the roles which require the basic quantum knowledge attained through one or two courses, the criteria for professional experience needed for job vacancies are comparatively lower for PhD graduates who have been trained in specialized quantum capabilities [95].

While employers place a high value on essential technical abilities (such as knowledge in science, engineering, math, or coding) and soft skills (such as communication, decision-making, and problem solving), they are more likely to invest in strengthening employees having industry-specific knowledge or job-specific skills.

In [95], it is suggested that the academic educational programs should be designed with multiple entry points with the prospect of building a satisfying career in the quantum industry, for example – pre-college exposure, undergraduate, graduate degrees and field training, and certificate programs for postgraduates. Combining traditional learning in specialized academic disciplines and shorter-term hands-on training with real-world projects will be critical in developing the skills needed for in-demand jobs. This adaptable approach to training learners at several entrance points enables them to transfer rapidly into the labor market because aside from acquiring fundamental knowledge, with practical activities and real projects, soft skills would be developed at a considerable level.

Skills evaluation. A world-wide known concept for assessing the capacity of performing job’s tasks is the concept of competence, which is integrated by knowledge, skills, abilities, and values (attitudes). Our work is attending only knowledge and skills; however, abilities are inherently involved in exhibiting proficiency.

Literature review shows some proposals to assess the possession of competence. A well-accepted scale for assessing proficiency is based in the EVELIN taxonomy [55], which has six levels of possession: remember, understand, explain, use, apply and develop (see Fig. 8).

Another scale is proposed by the European Commission, Directorate-General for Communications Networks, Content and Technology [74], this is called “European Competence Framework for Quantum Technology” (ECFQT), which emphasizes the time of training or study the set of concepts involved in quantum computing as well as the corresponding practice of those concepts. In Fig. 12 (see in APPENDIX C) we put together ECFQT and EVELIN; the combination of both provides guidance for assessing the level of proficiency of the workforce.

Fig. 12. [Images not available. See PDF.]

ECFQT and EVELIN scales.

DISCUSSION

Main findings:

• There is a proliferation of jobs and positions on quantum computing. Most of these jobs are absorbed by physics specialists.

• The literature review revealed a wide range of quantum knowledge citations. There is a coverture of the essential concepts of quantum topics, as well as topics from related disciplines. The umbrella of knowledge starts from QIST, deriving quantum mechanics, mathematics, information science, computer science, electronics and related disciplines.

• Several efforts have been made in academy and educational bodies to prepare students and professionals in quantum computing, as well as to design guidelines for designing courses and training materials. However, still there is no consensus about the contents and the depth levels.

• Even when there is no consensus on the set of topics to be included in quantum computing courses, there are several proposals on setting the core topics of quantum computing. Some studies reported success in teaching quantum computing to undergraduate and master levels. Mostly PhD programs are providing workforce to industry.

• Literature review reveals that soft skills are especially important for the multidisciplinary nature of quantum computing. Practitioners of quantum computing and quantum software engineering should interact with multidisciplinary teams, combining both quantum computing knowledge and soft skills.

Concerning findings:

• In industry, there is not a standard for specifying the requirements for a job position in quantum computing. In most cases, the quantum computing skills are not explicitly indicated.

• In the academic context, there is no consensus about the set of topics to be included in a quantum computing course. So, it is important to continue working on precising the core knowledge involved in quantum computing to design more structured courses that can be replicated in universities and training bodies.

• Most effort on teaching quantum computing is focused on graduate programs. However, bachelor’s graduates are required to play technical positions.

CONCLUSIONS

Quantum computing is a new emerging field that has the potential to dramatically change the way we think about computation and programming. The complexity inherited from quantum mechanics makes quantum computing difficult to attend by professionals not trained in physics [72].

The challenge for computer scientists and other professionals is to develop new programming techniques appropriate for quantum computers. Quantum entanglement and phase cancellation introduce a new dimension to computation. Programming no longer consists of merely formulating step-by-step algorithms but requires new techniques of adjusting phases and mixing and diffusing amplitudes to extract useful output. Software engineers and programmers should have a strong set of knowledge and technical skills on quantum-related topics and a new mindset for implementing quality quantum software.

Currently, most of the quantum computing positions in the labor market are taken by physics experts. It is time to bring possibilities to computer science professionals such as software engineers and programmers to face the challenges that quantum computing imposes.

A crucial challenge of workforce development is to offer courses with quantum computing skills that are in demand on adequate theoretical foundations to diverse student groups in universities and colleges that are not highly selective [96].

At the current stage of the second quantum revolution, working in the industry and development of quantum computers still generally requires a PhD. But a growing set of “quantum-adjacent” industry jobs also require quantum literacy. Those jobs include programming, software development, algorithms, electronics, cryogenics, and vacuum technology [37]. Based on this, to develop a skilled workforce required by quantum computing industry, curricula guidelines for creating undergraduate educational programs in QIST are required.

Several initiatives have emerged in creating curricula guidelines and educational programs; however, the authors emphasize the complexity of the fact of integrating quantum computing courses into the curricula of computer science, engineering, and related programs to address future workforce development issues. Despite these initiatives, there is no consensus about the topics to be included in a course and course sequencing.

Trying to contribute to this necessity, in this report, we present a literature review supported by systematic mapping, which allowed us to highlight the following issues:

(1) A complete set of knowledge related to quantum computing, involving basics concepts of physics, quantum mechanics, quantum information science, mathematics, computer science, and related disciplines.

(2) A set of technical skills (related to fundamental concepts of quantum computing), with a description for specific abilities related to quantum computing competences. These skills are called technical or hard skills.

(3) A set of soft skills, emphasizing skills required by software industry, but also including some specific skills required by the nature of quantum computing.

Contributions. The main contribution of this work is putting all together the core quantum computing knowledge, the technical skills and the related soft skills, which empower practitioners to work on quantum computing. These three elements allow academics and trainers to design curricula blocks and courses, having a panoramic view of a wide spectrum of quantum related topics.

Future work. Several proposals have been presented which try to integrate quantum computing topics in separate courses or curricula blocks in educational programs such as information technology, software engineering or computer science related. However, there are no specific proposals for well-structured curriculum guidelines, such as SWEBOK for classical Software Engineering.

The next initiatives are formulated considering the necessity of guidelines for developing skills in quantum computing and a well-prepared workforce for this prominent industry.

(1) Determining the depth and complexity of quantum topics to be taught on each academic level. To do a systematic literature review about the quantum mechanics and quantum computing topics included in courses or curriculum at different levels: secondary school, high school, undergraduate, and graduate levels. The complexity and depth of topics are important factors for teaching quantum knowledge at different educational levels. So, it is important to assess the effectiveness of the set of knowledge taught in terms of the depth managed, and the pedagogic practices used.

(2) To map the results of this research with the more recent versions of the SWEBOK. In the best of our knowledge, existing curricula guidelines such as SWEBOK, do not include specific topics of emergent trends such as quantum computing. Our proposal promotes including quantum computing topics in SWEBOK. This is a significant complement due to the core of quantum computing implementation is based on quantum mechanics and mathematical background required. This fact could represent a revisited version of the foundations considered in the SWEBOK topics structure.

ACKNOWLEDGMENTS

We would like to thank Centro de Investigación en Matemáticas (CIMAT A.C.) for their support in providing access to electronic databases. Also, we would like to thank Universidad Autónoma de Baja California, for financing this research through the Project 3908_300/6/C/63/23 “Computación Cuántica: Implicaciones en la Ingeniería de Software y las Competencias del Ingeniero de Software,” 23a

Convocatoria Interna de Proyectos de Investigación. Finally, thanks to the team Red Mexicana de Ingeniería de Software (REDMIS) who participated in this project and literature review.

FUNDING

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

CONFLICT OF INTEREST

The authors of this work declare that they have no conflicts of interest.

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

AI tools may have been used in the translation or editing of this article.

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