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IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT 1
Evolution of Quantum Computing: Theoretical and
Innovation Management Implications for
Emerging Quantum Industry
Mario Coccia , Saeed Roshani , and Melika Mosleh
Abstract—Quantum computing is a vital research field in science
and technology. One of the fundamental questions hardly known
is how quantum computing research is developing to support sci-
entific advances and the evolution of path-breaking technologies
for economic, industrial, and social change. This study confronts
the question here by applying methods of computational scien-
tometrics for publication analyses to explain the structure and
evolution of quantum computing research and technologies over
a 30-year period. Results reveal that the evolution of quantum
computing from 1990 to 2020 has a considerable average increase of
connectivity in the network (growth of degree centrality measure),
a moderate increase of the average influence of nodes on the flow
between nodes (little growth of betweenness centrality measure),
and a little reduction of the easiest access of each node to all other
nodes (closeness centrality measure). This evolutionary dynamics
is due to the increase in size and complexity of the network in
quantum computing research over time. This study also suggests
that the network of quantum computing has a transition from
hardware to software research that supports accelerated evolution
of technological pathways in quantum image processing, quantum
machine learning, and quantum sensors. Theoretical implications
of this study show the morphological evolution of the network in
quantum computing from a symmetric to an asymmetric shape
driven by new inter-relatedresearch fields and emerging technolog-
ical trajectories. Findings here suggest best practices of innovation
management based on R&D investments in new technological di-
rections of quantum computing having a high potential for growth
and impact in science and markets.
Index Terms—Innovation management, quantum algorithms,
quantum computing (QC), quantum network, technological
change, technological paradigm, technological trajectories.
I. INTRODUCTION
QUANTUM computing (QC) research can improve infor-
mation and communication technologies by allowing the
Manuscript received November 25, 2021; revised March 24, 2022; accepted
April 22, 2022. Review of this manuscript was arranged by Department Editor
F. Tietze. (Corresponding author: Mario Coccia.)
Mario Coccia is with the National Research Council of Italy, Collegio
Carlo Alberto, Via Real Collegio, 30–10024 Moncalieri (Torino), Italy (e-mail:
mario.coccia@cnr.it).
Saeed Roshani is with the Allameh Tabataba’i University, Department of
Technology and Entrepreneurship Management, Tehran 14896-84511, Iran (e-
mail: roshani@atu.ac.ir).
Melika Mosleh is with the Birmingham Business School, College of Social
Sciences, University of Birmingham, B15 2SQ Birmingham, U.K. (e-mail:
mxm1219@alumni.bham.ac.uk).
Color versions of one or more figures in this article are available at
https://doi.org/10.1109/TEM.2022.3175633.
Digital Object Identifier 10.1109/TEM.2022.3175633
transmission and manipulation of quantum bits (or qubits, which
is the quantum mechanical analog of a classical bit) between
remote locations [1]. QC is at the initial stage of technological
evolution but has a high potential of generating innovations
in quantum communication, quantum cryptography, quantum
optics, etc. to support competitive advantage of firms and nations
[2]–[6]. The evolution of QC needs R&D investments for cre-
ating a complete and functional quantum ecosystem—based on
effective scientific and technological networks, reliable physical
infrastructures, skilled human resources, etc.—that supports sci-
entific advances and innovations in markets and society [7]–[11].
There is a vast literature in these research fields, however,
the evolution of QC that develops path-breaking innovations
is hardly known. This study confronts the problem here by
developing a computational analysis based on publications over
1990–2020 period to explain the structure and evolution of QC
research that support scientific and technological trajectories
having implications for economic, industrial, corporate, and
social change. This study can detect the main QC technologies,
which may be major sources of competitive advantage for firms
and nations to solve complex problems and satisfy new needs
of people in society. In this context, the next section presents a
theoretical framework to describe how maps of science, which
we are going to create for QC, can explain the evolution of new
technologies over the course of time.
II. THEORETICAL FRAMEWORK
Scholars assert that the evolution of technologies is increas-
ingly based on the interaction between technologies and sci-
entific fields that generate co-evolutionary pathways of new
technological trajectories [12]–[20]. In general, the evolution
of technologies is driven by science that is often viewed as
a self-organizing system with various scientific changes and
interactions within and between social community of scholars
[21]–[22]. The scientific development, underlying technological
change, can be investigated with publications that are a main unit
of analysis to show science maps of how scientific fields and
technologies evolve over time [23]–[26]. In this context, Ley-
desdorff (2007) has developed a map of the whole set of journals,
showing how centrality measures can clarify the environment of
citations given by small sets of journals where citing is above
a certain threshold [27]. Savov et al. [28] propose an approach
of citation-based measures to identify breakthrough scientific
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2IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT
Fig. 1. Data processing procedure of this study.
papers driving science advances. Instead, Boyack et al. [29]
study the accuracy of scientific maps using eight different inter-
citation and co-citation similarity metrics. Klavans and Boyack
[30] identify a better measure of relatedness for mapping science
because the measurement of the relatedness between bibliomet-
ric units (e.g., journals, words, etc.) provides critical aspects for
structure and evolution of science. Relatedness measures have
also a vital role in showing the relationship between data items
in maps [30]. Small and Garfield [31] reveal that large and small
areas of science are often arranged in center-periphery patterns.
Small argues that the network of linkages from document to
document and from discipline to discipline can show crossover
fields and offer the possibility of exploring extended pathways of
knowledge and new technological trajectories [32]. Boyack and
colleagues also maintain that maps of science can identify major
fields of research and emerging technologies, showing their size
and interconnectedness [29]. The results of these studies can
guide R&D investments and innovation strategy of firms and
governments for supporting their competitive advantage in tur-
bulent markets [33]–[37]. The evolution of emerging technolo-
gies, as anticipated, is also associated with underlying scientific
development and change [33]. Cozzens and colleagues point
out that emerging technologies present new opportunities for
national competitive advantage [38]–[39]. Manifold techniques
have been developed in scientometrics to detect and analyze new
domains in science and technology [24]–[43]. These methods
are based on large datasets and computational approaches based
on complex indicators for detecting new technological trajec-
tories using data from publications and/or patents [44]–[46]. In
particular, quantitative approaches based on bibliometric data
of journals, compared to patents, can capture information of
innovations early in their technological development ([26], [38],
[39]). In this context, Deshmukh and Mulay [47] show that the
maximum number of publications in the field of QC is in physics,
astronomy, and computer science. However, studies of sciento-
metrics concerning evolutionary networks of QC associated with
new technologies are scarce in the literature. This study endeav-
ors to create and analyze the mapping of QC over a 30-year time
frame to detect different stages of the structure of network and
the evolution of QC with main technological trajectories. The
next section presents the methodology to develop the purpose
of this study.
III. MATERIAL AND METHOD
Fig. 1 shows the methodological approach of the present
study based on: (1) data collection, (2) data processing, and (3)
exploration of networks in QC.
A. Data Collection and Sample
We used the Web of Science-WOS core collection database
for extracting the articles related to QC [48]. To collect the most
relevant articles in this field of research, we searched “Quantum
Comput∗” through the topics of articles. Afterward, the results
were limited to document type =(“Articles”), language =
(“English”), Web of Science index =(“Science Citation Index
Expanded”) to gather helpful data. Data are over the 1990–2020
period. The sample contains 14,132 articles split into three
timespans, given by 1990–2000, 2001–2010, and 2011–2020.
B. Data Processing and Analysis
First, we used original keywords of articles (DEs) tag as the
basis for detection of technologies related to QC. Among Web of
Science’s special tags, “DE” is one that is related to the author’s
keywords and can be used to build a keyword co-occurrence
network. Web of Science provides another source of keywords
that are related to the keyword plus (IDs) that Web of Science
database assigns to the documents [48]. Hence, in this article,
the units of analysis are the original keywords (DEs) of articles
provided by authors to find the QC research fields and technolo-
gies and to create the interconnection network among nodes.
Second, we have done the cleaning of data for constructing
the networks. We kept only the key phrases combined with the
word “quantum.” We also merged all keywords with the same
meaning written in different structures, including abbreviation,
plural, and singular forms, and we put the gerund and noun forms
together and considered them as one single node. Additionally,
we eliminated the isolated nodes, which have no connections
with other nodes in the graph.
C. Creation and Exploration of Networks
Finally, we generated co-occurrences networks by SCI2 Tool
V.1.3 software [49] and imported them as a GraphMl format file
into Gephi software version 3.6.5 [50] to visualize and analyze
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COCCIA et al.: EVOLUTION OF QC: THEORETICAL AND INNOVATION MANAGEMENT IMPLICATIONS 3
TAB L E I
COMPARISON OF NETWORK MEASURES AND INDICATORS OVER THREE PERIODS
Note: Nodes represent vertices in a graph; links (or edges) are connections between nodes (or vertices) of the network. Graph density is the maximum number of existed edges
divided by the number of edges; Avg. path length is the number of steps in average, through the shortest routes between all joints of network nodes.
the networks for each period under study (from 1990 to 2000,
2001 to 2010, and 2011 to 2020). The structure of networks
is based on nodes and edges. In the keywords co-occurrences
network, each node represents subtopics related to QC research
and technologies. An edge represents a linkage between two
keywords when they appear in the same document. The thickness
of each edge indicates the frequency of appearance of a specific
node with other connected nodes in documents, i.e., when the
edge of nodes AB is thicker than the edge of nodes AC, the
co-occurrences frequency between node A and node B is higher
than the frequency of the link between node A and node C.
Moreover, SCI2 Tool is applied to calculate metrics of these
networks, such as degree centrality (DC), betweenness centrality
(BC), and closeness centrality (CC) measures to explore the
evolutionary behavior of different nodes within the network of
QC over time. In particular,
a) DC is the number of connected edges to a node [51]. DC
indicates the number of connections (connectivity) in the
network of keywords.
b) BC indicates the amount of influence or control a node
has over the flow between nodes and networks (similar to
a bridge). This index represents the importance of a node
in making the connection between other network nodes
and is responsible for sustaining the network integration
[52]. We implemented BC measures to show the bridge
nodes that facilitate the linkage of entities.
c) A node’s CC is an indicator of a network centrality,
defined as the number of links needed to connect each
node in the network with all the other nodes in the net-
work or the average number of links required to reach all
other nodes in the network from a node in the network
[53].
These measures provide comprehensive information for a
comparative analysis of the evolutionary pathways of networks
in QC over time [54]–[55].
IV. RESULTS
Table I shows that the interconnection of QC-related words is
structured in the 1990–2000 period through 87 nodes and 140
edges based on 668 articles (cf., Fig. 2). The graph density of
this network is 0.037, which respectively shows a considerable
integration belongs to the network. Between 2001 and 2010,
based on 5,224 publications, the number of nodes increased by
4.48 times (it is 477), and the number of edges increased by 4.66
times (the number is 793) with also a reduction in graph density,
which is 0.007 in the second period under study (see Fig. 3). In
the last period, 2011–2020, the number of nodes increased by
1.21 times compared to the previous period. This graph has a
density of 0.004, which is less than the graph density of 2001–
2010 network (see Fig. 4). The average path length of the last
period graph is 2.859, a higher value than the two other periods.
Interestingly, the interconnection network contains 2,244 edges
between 2011 and 2020, with an increase of 1.83 times over the
preceding decade.
A. Evolution of Network in QC Research from 1990 to 2000
In the first period, Table II and Fig. 2 show that quantum com-
puter and quantum Turing machines have the highest DC. These
findings show that these nodes have a main role in structuring
the graph and establishing new linkages with different nodes in
that period, which caused the highest level of connection score.
Meanwhile, QC (item) with the BC of 0.486 and quantum com-
puter with 0.118 established essential bridges among other net-
work nodes to facilitate the interaction and coevolution between
different topics [16]. Furthermore, Fig. 2 shows that QC node
has the intertwined connection with the quantum algorithm,
quantum information, and quantum dot. Instead, quantum turing
machine with a high centrality degree has a strong connection
with quantum polynomial time. In this network, quantum optics,
quantum searching, quantum lattice gas, quantum quantitates,
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4IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT
Fig. 2. Evolution of interconnection in the QC-related words, 1990–2000 period.
quantum logic, and quantum communication also illustrate a
significant connection with QC node.
B. Evolution of Network in QC Research from 2001 to 2010
In the 2001–2010 period, the quantum network has a great
expansion. In this regard, Table II shows that quantum infor-
mation and quantum algorithms grasped the highest level of
DC after QC and quantum computer. Moreover, the node of the
quantum turing machine is eliminated from the top nodes. As
far as BC is concerned, quantum dot with a value of 0.162 had a
significant role in bridging the network. This node has BC value
that is more than twice of the quantum computer, while its DC
value is less than a half of the quantum computer. According
to Table II (2001–2010 period) and Fig. 3, there is a strong and
established linkage between nodes of quantum information and
QC. Quantum information in the first period utilized its initial
connections with QC to grow faster; after ten years, it is one of
the central nodes with the highest value of DC. Moreover, Fig. 3
shows that quantum gate and quantum dot have created new
strong linkages with the node of quantum computer, creating
potential characteristics of coevolution over the course of time.
In addition, Fig. 3 shows an interesting triangle connection
pattern between quantum optics, quantum entanglement, and
quantum communications, which is a starting point of intensive
interaction and rapid coevolution pathways between these nodes
in the evolution of QC network.
C. Evolution of Network in QC Research from 2011 to 2020
In the period from 2011 to 2020, Table II and Fig. 4 show
that quantum algorithm has been experiencing a considerable
growth in the DC measure. In this period, it has expanded
even more than quantum computer and can be considered the
second highest DC node in the interconnection network of
QC. Moreover, during this period, quantum information and
quantum correcting-error code have a higher DC value than
quantum computer: this result shows the growing importance of
software development in QC. In fact, these results also illustrate
a transition of QC research from hardware to software aspects
in evolutionary development. Although quantum algorithm and
quantum information have the highest DC and expand their
connections through the evolution of network, they still have
a weaker bridging role compared to quantum computer, such
that these nodes cannot establish their essential role to facilitate
the connections among other nodes. This finding suggests that
they are in the initial phase of technological growth, but their BC
has potential factors for growth in a not-too-distant future; es-
pecially, quantum algorithm and quantum information will play
an essential role in establishing an integrated evolution within
network of QC research. Moreover, in this period, quantum
processing and quantum circuit are new nodes that started their
connection with QC. This scientific change in linkages and nodes
shows a continuous transition and evolution of this scientific
domain.
D. General Evolution of the Network in QC Research and
Emerging Technologies for Innovative Applications in Markets
An in-depth technology analysis within the network of QC
shows that in the period 1990—2000, the highest connectivity
is due to nodes of quantum turing machine (DC =9) and
quantum information (DC =8), in addition, of course to main
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COCCIA et al.: EVOLUTION OF QC: THEORETICAL AND INNOVATION MANAGEMENT IMPLICATIONS 5
Fig. 3. Evolution of interconnection in the QC-related words, 2001–2010 period.
nodes of QC and quantum computer. In 2001–2010 period, the
highest connectivity is driven by quantum information with a
considerably increase of DC =45 and quantum algorithm having
DC =41. In the last period (2011–2020), the acceleration of
connectivity is due to quantum algorithm (DC =102), quantum
information with DC =90, and the new entry of quantum
error-correcting code (DC =65). These evolutionary aspects
of QC research suggest, as said, a transition from hardware
to software characteristics of the science dynamics. In this
scientific and technological evolution, the nodes having a high
influence or control over the flow between nodes in the network
are, in 1990–2000 period, the QC, quantum computer, quantum
entanglement, and quantum information processing, whereas in
the 2011–2020 period, they are QC, quantum computer, and
new entry of quantum algorithm and quantum information.
Finally, CC suggests that nodes having the easiest access to
all other nodes in the network, over 1990–2000 period, are
quantum lattice gas, quantum jumps, quantum state diffusion,
and quantum trajectories; over 2001–2010 period, main nodes
are QC, quantum computer, quantum information, and quantum
algorithm; finally, in the last period of 2011–2020, we have quan-
tum mechanics, quantum annealing, quantum image processing,
and quantum dot with a high CC measure. A general technology
analysis of the evolution of the top 20 fields and technologies in
QC from 1990 to 2020 shows a considerable average increase of
connectivity with a growth of 7.43 (DC), a moderate increase of
0.12 (BC) about the average influence or control of nodes on the
flow between nodes within network, whereas CC measure has a
very low reduction—0.06 (the average easiest access of nodes to
all other nodes in technological network for top 20 QC research
and technologies under study). This evolutionary dynamics is
due to the increase in size and complexity of the technological
and scientific network in QC (see Table III).
The emerging technologies in QC from 2001 to 2010 are
(see Table IV): quantum memory, adiabatic QC, topological
QC, quantum walk, and quantum wire. Furthermore, over 2011-
2020, the emerging technologies are quantum image processing,
quantum machine learning, and blind QC. This result suggests
the potential transfer of QC research in new technologies for
innovative applications, such as in quantum image processing
for creating quantum images because this new technology has
high technical performance in terms of computing speed, low
storage requirements, and high security [56]. Other emerging
technologies in QC research are quantum machine learning
based on the interaction of machine learning programs and
quantum algorithms [57] and blind QC, such that quantum
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6IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT
Fig. 4. Evolution of interconnection in the QC-related words, 2011–2020 period.
servers do not have full information about activities that users are
computing for high security of tasks. In this innovative activity,
a new direction is due to delegated QC in which users operate
on server’s resources for assessing a complex circuit without
leaking any information about the input to the server. Another
emerging technology is circuit quantum electrodynamics to ana-
lyze fundamental interaction between light and matter (quantum
optics), quantum internet for innovative communications by
teleportation, and quantum sensors that detect variations in mi-
crogravity for altering elements of the nature at the submolecular
level with main applications in microscopy, positioning systems,
mineral exploration, seismology, optical quantum sensors for
quantum lithography, etc. [58]–[59].
V. DISCUSSION WITH THEORETICAL AND INNOVATION
MANAGEMENT IMPLICATIONS
The evolution of QC network over the last three decades is
unparalleled [60]. Scholars have analyzed quantum research and
suggested main technological pathways that, of course, are not
exhaustive: (i) quantum information; (ii) quantum sensing and
imaging; (iii) quantum communication and cryptography; and
(iv) quantum computation [61]–[63]. In this research stream, the
study here shows the scientific and technological evolution of
network in QC over a 30-year period (from 1990 to 2020). Re-
sults show that the network of QC is rapidly growing from 2001
to 2020. In particular, this study suggests that the research fields
of QC are in continuous evolution because of recent advances
in physics, optics, and computer science. In fact, in the period
2001–2010, a lot of new technologies emerged, developed, and
connected to other ones, such as quantum memory, adiabatic
QC, topological QC, quantum walk, quantum wire, quantum
programming language, and quantum cellular automata. In addi-
tion, emerging technologies over 2011–2020 period are focused
on quantum image processing, quantum machine learning, blind
QC, delegated QC, circuit quantum electrodynamics, and quan-
tum image representation [64]. These findings here reveal that
the dynamics of QC research evolves with endogenous processes
of high connectivity between research fields and technologies
that increase the size and complexity of the quantum computing
network supporting research fields, scientific and technological
trajectories [22].
A. Principal Theoretical Implications from the Evolution of
QC network
These results suggest some properties of the scientific and
technological change of the network of QC research that can
support general principles for the evolution of science and
technology.
First, QC research co-evolves with complex interactions
driven by three evolutionary characteristics: a) a high con-
nectivity between nodes of research fields and technologies;
b) moderate growth of the average influence of nodes on the
flow between nodes within network; c) a reduction about the
average easiest access of nodes to all other nodes because of
a larger size and complexity of QC network over the course of
time.
Second, some research fields and technologies in QC network
have a critical position, playing a role of master entity for
connections of manifold research fields and technologies, such
as quantum algorithm and information.
Third, QC network is generating, during the co-evolution of
research fields, new technological trajectories from a process
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COCCIA et al.: EVOLUTION OF QC: THEORETICAL AND INNOVATION MANAGEMENT IMPLICATIONS 7
TAB L E I I
NETWORK MEASURES IN QUANTUM COMPUTING RESEARCH AND TECHNOLOGIES FROM 1990 TO 2020
Note: Degree Centrality (DC) indicates number of connections (connectivity); Betweenness Centrality (BC) indicates the amount of influence or control a node has
over the flow between nodes and networks (similar to a bridge); Closeness Centrality (CC) indicates the easiest access to all other nodes in a network or sub-network
(shortest distance from nodes).
of specialization in science, such as quantum machine learning,
blind QC, quantum sensor, quantum image processing, etc.
Fourth, the morphological evolution of network in QC re-
search is changing from spheroid shape in the initial stage of
evolution to an irregular shape in the stage of growth over
2011–2020 period (see Fig. 5).
rSpheroid type (1990–2000 period) is a scientific and tech-
nological network in the initial phase of evolution having
a symmetric shape with nodes and mutual interconnexions
sparse.
rIrregular type (2011–2020 period) is a scientific and tech-
nological network in the growing phase of evolution with
an asymmetric shape having dense nodes, high mutual
interconnexions, and high connectivity. Inside the scien-
tific and technological network, the evolution is based
on endogenous processes given by: merger when two or
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8IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT
TABLE III
PATTERN OF THE EVOLUTION OF QUANTUM COMPUTING RESEARCH FROM 1990 TO 2020, BASED ON TOP 20 FIELDS AND TECHNOLOGIES OF TABLE II
Note: Degree Centrality (DC) indicates number of connections (connectivity); Betweenness Centrality (BC) indicates the amount of influence or control a node has
over the flow between nodes and networks (similar to a bridge); Closeness Centrality (CC) indicates the easiest access to all other nodes in a network or subnetwork
(shortest distance from nodes).
Fig. 5. Morphological evolution of network in QC research.
more nodes (technologies or scientific fields) combine their
elements or subsystems to generate a new large system;
interacting pair when two nodes interact with a beneficial
coevolution having aspects of mutualism and symbiosis
over time; finally, splitting when a node grows for the
accumulation of scientific research and causes a split off
of some subsystems, generating two or more new nodes
(independent systems of new research fields and technolo-
gies).
B. Principal Implications of Innovation Policy and Innovation
Management for a Quantum Industry
The evolutionary pathways in QC have main implications
for the management of technologies and innovations to sup-
port decisions of R&D investments of firms and governments
for competitive advantage in markets. In fact, policymakers
and R&D managers know that financial resources can be an
accelerator factor for progress and diffusion of science and tech-
nology to support the scientific and technological development
in society [65]. This study shows critical research fields and
technologies in QC that are growing with a higher DC measure;
R&D management can allocate economic resources towards
these research fields and technologies (e.g., quantum memory,
quantum image processing, quantum machine learning, etc.) to
support scientific and technological development that create a
background for competitive advantage in markets. In addition,
policymakers and funding agencies can use these findings here
for making efficient decisions of sponsoring specific research
fields and technologies in QC to foster technology transfer
having fruitful effects for economic growth and social change
in nations.
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COCCIA et al.: EVOLUTION OF QC: THEORETICAL AND INNOVATION MANAGEMENT IMPLICATIONS 9
TAB L E I V
TOP 20 EMERGING QUANTUM COMPUTING TECHNOLOGIES FROM 2001 TO 2020
VI. CONCLUSION
The evolution of QC research shows that from 2001 to 2020
the number of nodes has a continuous growth, increasing the
connectivity between nodes and increasing nodes that control the
flow between nodes. The evolution of network in QC shows that
new research fields and technologies emerge, such as quantum
image processing, quantum machine learning, etc. Moreover,
the morphological evolution of network in QC has changing
shape from a spheroid typology in the initial phase of evolution
(1990–2000) with sparse nodes and lower interconnections to
an irregular type in the phase of growth with a high density of
nodes and intensive interactions between nodes that generate an
asymmetric shape with large dominant nodes, such as quantum
information, quantum algorithm, etc., generating the continuous
expansion of the domain of this research field in the universe of
science (see Fig. 5). Results also reveal that network of QC
research is evolving with a transition from hardware to software
aspects.
These conclusions are, of course, tentative. Although this
study has provided some interesting, albeit preliminary results,
as many other bibliometric studies, it has several limitations.
First, the precision of the search queries is affected by ambivalent
meanings in QC, such as information, computing, computer,
etc. Second limitation of this study is that the sources under
study may only capture certain aspects of the ongoing evo-
lutionary dynamics of QC research. Third, there are multiple
confounding factors that could have an important role in the
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10 IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT
dynamics of QC research to be further investigated, such as
multiple discoveries [66], R&D investments, role of scientific
institutions, collaboration intensity, intellectual property rights,
etc. [67]–[73]. Fourth, the network of QC research changes its
borders during the evolution of science, and as a consequence,
the morphology of network during the evolution, generating an
irregular and complex shape, such that the identification of stable
technological trajectories and scientific fields over the course of
time is a difficult exercise.
To conclude, future research should consider new data when
available and apply newapproaches to reinforce proposed results
here. The future development of this study is also directed to
design indices of technometrics based on measures of between-
ness, closeness, and DC of networks to assess technological and
scientific change, to predict the emergence of new technological
trajectories, as well as to support further implications for the
management of technology and R&D management. Despite
these limitations, the results presented here clearly illustrate the
main evolutionary paths of QC research that are increasingly
based on growing connectivity between technologies and re-
search fields, but a further detailed examination is needed for
explaining the driving factors of the technological evolution and
supporting an appropriate strategic management of innovation
that supports a new quantum industry for the competitive advan-
tage of firms and nations in turbulent markets.
REFERENCES
[1] W. Kozlowski and S. Wehner, “Towards large-scale quantum networks,”
in Proc. 6th Annu. ACM Int. Conf. Nanoscale Comput. Commun., 2019,
pp. 1–7.
[2] J. Atik and V. Jeutner, “Quantum computing and computational law,” Law,
Innov. Technol., vol. 13, no. 2, pp. 302–324, 2021.
[3] M. Coccia and M. Bellitto, “Human progress and its socioeconomic effects
in society,” J. Econ. Social Thought, vol. 5, no. 2, pp. 160–178, 2018.
[4] A. Dahlberg et al., “A link layer protocol for quantum networks,” in Proc.
ACM Special Int. Group Data Commun., 2019, pp. 159–173.
[5] M. Möller and C. Vuik, “On the impact of quantum computing technology
on future developments in high-performance scientific computing,” Ethics
Inf. Technol., vol. 19, no. 4, pp. 253–269, 2017.
[6] D. Carberry et al., “Building knowledge capacity for quantum com-
puting in engineering education,” Comput. Aided Chem. Eng., vol. 50,
pp. 2065–2070, 2021.
[7] K. Batra et al., “Quantum machine learning algorithms for drug discovery
applications,” J. Chem. Inf. Model., vol. 61, no. 6, pp. 2641–2647, 2021.
[8] H. Hou and Y. Shi, “Ecosystem-as-structure and ecosystem-as-
coevolution: A constructive examination,” Technovation, vol. 100, 2021,
Art. no. 102193.
[9] O. Granstrand and M. Holgersson, “Innovation ecosystems: A conceptual
review and a new definition,” Technovation, vol. 90, 2020, Art. no. 102098.
[10] M. Pande and P. Mulay, “Bibliometric survey of quantum machine learn-
ing,” Sci. Technol. Libraries, vol. 39, no. 4, pp. 369–382, 2020.
[11] P. Rao, K. Yu, H. Lim, D. Jin, and D. Choi, “Quantum amplitude estima-
tion algorithms on IBM quantum devices,” Quantum Commun. Quantum
Imag., vol. 11507, pp. 49–60, 2020.
[12] L. Ardito, M. Coccia, and A. Messeni Petruzzelli, “Technological exapta-
tion and crisis management: Evidence from COVID-19 outbreaks,” R&D
Manage., vol. 51, no. 4, pp. 381–392, 2021.
[13] L. Benamar, C. Balagué, and Z. Zhong, “Internet of things devices appro-
priation process: The dynamic interactions value appropriation (DIVA)
framework,” Technovation, vol. 89, 2020, Art. no. 102082.
[14] M. Coccia, “Spatial relation between geo-climate zones and technological
outputs to explain the evolution of technology,” Int. J. Transitions Innov.
Syst., vol. 4, no. 1–2, pp. 5–21, 2015.
[15] M. Coccia, “Technological innovation,” Innovations, The Blackwell En-
cyclopedia of Sociology, G. Ritzer and C. Rojek, Eds., John Wiley &
Sons, Ltd., vol. 11, 2021, pp. 299–317, doi: 10.1002/9781405165518.
wbeost011.pub2.
[16] M. Coccia and J. Watts, “A theory of the evolution of technology: Techno-
logical parasitism and the implications for innovation magement,” J. Eng.
Technol. Manage., vol. 55, 2020, Art. no. 101552.
[17] M. Coccia, S. Roshani, and M. Mosleh, “Scientific developments and new
technological trajectories in sensor research,” Sensors, vol. 21, no. 23,
2021, Art. no. 7803.
[18] M. Coccia and U. Finardi, “New technological trajectories of non-thermal
plasma technology in medicine,” Int. J. Biomed. Eng. Technol., vol. 11,
no. 4, pp. 337–356, 2013.
[19] E. S. Kashani and S. Roshani, “Evolution of innovation system literature:
Intellectual bases and emerging trends,” Technological Forecast. Social
Change, vol. 146, pp. 68–80, 2019.
[20] M. Jovanovic, D. Sjödin, and V. Parida, “Co-evolution of platform ar-
chitecture, platform services, and platform governance: Expanding the
platform value of industrial digital platforms,” Technovation, Jan. 2021,
Art. no. 102218.
[21] K. Börner, “Science of science studies: Sci2 tool,” Commun. ACM, vol. 54,
no. 3, pp. 60–69, 2011.
[22] X. Sun and J. Kaur, C. S. Milojevi, A. Flammini, and F. Menczer, “Social
dynamics of science,” Sci. Rep., vol. 3, 2013, Art. no. 1069.
[23] K. Boyack, K. Börner, and R. Klavans, “Mapping the structure and
evolution of chemistry research,” Scientometrics, vol. 79, no. 1, pp. 45–60,
2009.
[24] L. Leydesdorff, “Various methods for the mapping of science,” Sciento-
metrics, vol. 11, no. 5–6, pp. 295–324, 1987.
[25] F. Narin, M. Carpenter, and N. C. Berlt, “Interrelationships of scientific
journals,” J. Amer. Soc. Inf. Sci., vol. 23, no. 5, pp. 323–331, 1972.
[26] Z. Liang, J. Mao, K. Lu, Z. Ba, and G. Li, “Combining deep neural network
and bibliometric indicator for emerging research topic prediction,” Inf.
Process. Manage., vol. 58, no. 5, 2021, Art. no. 102611.
[27] L. Leydesdorff, “Betweenness centrality as an indicator of the interdisci-
plinarity of scientific journals,” J. Amer. Soc. Inf. Sci. Technol., vol. 58,
no. 9, pp. 1303–1319, 2007.
[28] P. Savov, A. Jatowt, and R. Nielek, “Identifying breakthrough scientific
papers,” Inf. Process. Manage., vol. 57, no. 2, 2020, Art. no. 102168,.
[29] K. W. Boyack, R. Klavans, and K. Börner, “Mapping the backbone of
science,” Scientometrics, vol. 64, no. 3, pp. 351–374, 2005.
[30] R. Klavans and K. Boyack, “Identifying a better measure of relatedness for
mapping science,” J. Amer. Soc. Inf. Sci. Technol., vol. 57, pp. 251–263,
2006.
[31] H. Small and E. Garfield, “The geography of science: Disciplinary and
national mappings,” J. Inf. Sci., vol. 11, no. 4, pp. 147–159, 1985.
[32] H. Small, “Visualizing science by citation mapping,” J. Amer. Soc. Inf.
Sci., vol. 50, no. 9, pp. 799–813, 1999.
[33] S. F. Carley, N. C. Newman, A. L. Porter, and J. G. Garner, “An indica-
tor of technical emergence,” Scientometrics, vol. 115, no. 1, pp. 35–49,
2018.
[34] M. Coccia, “Sources of technological innovation: Radical and incremental
innovation problem-driven to support competitive advantage of firms,”
Technol. Anal. Strategic Manage., vol. 29, no. 9, pp. 1048–1061, 2017.
[35] M. Coccia, Fundamental Interactions as Sources of the Evolution of
Technology, Working paper, Arizona University, Tucson, AZ, USA, 2017.
[36] H. Yalcin and T. Daim, “A scientometric review of technology capability
research,” J. Eng. Technol. Manage., vol. 62, 2021, Art. no. 101658.
[37] M. Zamani, H. Yalcin, A. B. Naeini, G. Zeba, and T. U. Daim, “Devel-
oping metrics for emerging technologies: Identification and assessment,”
Technological Forecast. Social Change, vol. 176, 2022, Art. no. 121456.
[38] S. Cozzens et al., “Emerging technologies: Quantitative identification
and measurement,” Technol. Anal. Strategic Manage., vol. 22, no. 3,
pp. 361–376, 2010.
[39] H. Ren and Y. Zhao, “Technology opportunity discovery based on con-
structing, evaluating, and searching knowledge networks,” Technovation,
vol. 101, 2021, Art. no. 102196.
[40] S. K. Arora, A. L. Porter, J. Youtie, and P. Shapira, “Capturing new
developments in an emerging technology: An updated search strategy
for identifying nanotechnology research outputs,” Scientometrics, vol. 95,
no. 1, pp. 351–370, 2013.
[41] K. W. Boyack, R. Klavans, H. Small, and L. Ungar, “Characterizing the
emergence of two nanotechnology topics using a contemporaneous global
micro-model of science,” J. Eng. Technol. Manage., vol. 32, pp. 147–159,
2014.
[42] W. Glänzel and B. Thijs, “Using ‘core documents’ for detecting and la-
belling new emerging topics,” Scientometrics, vol. 91, no. 2, pp. 399–416,
2012.
[43] A.van den Oord and A. VanWitteloostuijn, “A multi-level model of emerg-
ing technology: An empirical study of the evolution of biotechnology from
1976 to 2003,” PLoS One, vol. 13, no. 5, 2018, Art. no. e0197024.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
Authorized licensed use limited to: CAMBRIDGE UNIV. Downloaded on June 20,2022 at 20:41:17 UTC from IEEE Xplore. Restrictions apply.
COCCIA et al.: EVOLUTION OF QC: THEORETICAL AND INNOVATION MANAGEMENT IMPLICATIONS 11
[44] C. Chen, “CiteSpace II: Detecting and visualizing emerging trends and
transient patterns in scientific literature,” J. Amer. Soc. Inf. Sci. Technol.,
vol. 57, no. 3, pp. 359–377, 2006.
[45] J. Garner, S. Carley, A. L. Porter, and N. C. Newman, “Technological
emergence indicators using emergence scoring,” in Proc. Portland Int.
Conf. Manage. Eng. Technol., 2017, pp. 1–12.
[46] F. Moya-Anegón, B. Vargas-Quesada, V. Herrero-Solana, Z. Chinchilla-
Rodríguez, E. Corera-Álvarez, and F. J. Munoz-Fernández, “A new tech-
nique for building maps of large scientific domains based on the cocitation
of classes and categories,” Scientometrics, vol. 61, no. 1, pp. 129–145,
2004.
[47] S. Deshmukh and P. Mulay, “Quantum clustering drives innovations: A
bibliometric and patentometric analysis,” Quantum, Winter 1-1, pp. 1–27,
2021.
[48] “Web of Science (WOS).” Accessed: Sep. 15, 2021. [Online]. Available:
https://www.webofscience.com/wos/woscc/basic-search
[49] S.Team, “Science of science (Sci2) tool,”Indiana Univ. SciTechStrategies,
vol. 379, 2009.
[50] M.Bastian, S. Heymann, and M. Jacomy, “Gephi: An open source software
for exploring and manipulating networks,” in Proc. Int. AAAI Conf. Web
Social Media, 2009, vol. 3, no. 1, pp. 361–362.
[51] D. Sharma and A. Surolia, “Degree centrality,” in Encyclopedia of Systems
Biology, W. Dubitzky, O. Wolkenhauer, K.-H. Cho, and H. Yokota, Ed.
New York, NY, USA: Springer, vol. 558, 2013.
[52] Y. Jia, V. Lu, J. Hoberock, M. Garland, and J. C. Hart, “Edge v. node
parallelism for graph centrality metrics,” in GPU Computing Gems Jade
Edition. Amsterdam, The Netherlands: Elsevier, 2012, pp. 15–28.
[53] R. Goldstein and M. S. Vitevitch, “The influence of closeness centrality
on lexical processing,” Front. Psychol., vol. 8, 2017, Art. no. 1683.
[54] M. Coccia, “An introduction to the methods of inquiry in social sciences,”
J. Social Administ. Sci., vol. 5, no. 2, pp. 116–126, 2018.
[55] M. Coccia and I. Benati, “Comparative models of inquiry,” Global En-
cyclopedia of Public Administration, Public Policy, and Governance,
Springer International Publishing AG, Part of Springer Nature, 2018.
doi: 10.1007/978-3-319-31816-5_1199-1.
[56] F. Yan, A. M. Iliyasu, and P. Q. Le, “Quantum image processing: A review
of advances in its security technologies,” Int. J. Quantum Inf., vol. 15,
no. 03, 2017, Art. no. 1730001.
[57] M. Schuld, I. Sinayskiy, and F. Petruccione, “An introduction to quantum
machine learning,”Contemporary Phys., vol. 56, no. 2, pp. 172–185, 2015.
[58] C. L. Degen, F. Reinhard, and P. Cappellaro, “Quantum sensing,” Rev.
Modern Phys., vol. 89, no. 3, 2017, Art. no. 035002.
[59] L. Pezze, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein,
“Quantum metrology with nonclassical states of atomic ensembles,” Rev.
Modern Phys., vol. 90, no. 3, 2018, Art. no. 035005.
[60] T. Scheidsteger, R. Haunschild, L. Bornmann, and C. Ettl, “Bibliometric
analysis in the field of quantum technology,” Quantum Rep., vol. 3, no. 3,
pp. 549–575, 2021.
[61] J. P. Dowling and G. J. Milburn, “Quantum technology: The second
quantum revolution,” Philos. Trans. Roy. Soc. London. Ser. A, Math., Phys.
Eng. Sci., vol. 361, no. 1809, pp. 1655–1674, 2003.
[62] L. Jaeger, The Second Quantum Revolution,” From Entanglement to
Quantum Computing and Other Super-Technologies. New York, NY, USA:
Springer, 2018.
[63] G. L. Long, P. Mueller, and J. Patterson, Introducing Quantum Engineer-
ing, vol. 1, Hoboken, NJ, USA: Wiley, 2019, p. e6.
[64] B. Bilal, S. Ahmed, and V. Kakkar, “Quantum dot cellular automata: A
new paradigm for digital design,” Int. J. Nanoelectronics Mater.,vol.3,
no. 1, pp. 41–54, 2019.
[65] S. Roshani, M.-R. Bagherylooieh, M. Mosleh, and M. Coccia, “What is the
relationship between research funding and citation-based performance?
A comparative analysis between critical disciplines,” Scientometrics,
vol. 126, no. 9, pp. 7859–7874, 2021.
[66] M. Coccia, “Probability of discoveries between research fields to ex-
plain scientific and technological change,” Technol. Soc., vol. 68, 2022,
Art. no. 101874.
[67] M. Coccia and L. Wang, “Evolution and convergence of the patterns of
international scientific collaboration,”Proc. Nat. Acad. Sci., vol. 113, no. 8,
pp. 2057–2061, 2016.
[68] M. Coccia, “Metrics of R&D performance and management of public
research labs,” in Proc. Manag. Technologically Driven Org., Hum. Side
Innov. Change, 2003, pp. 231–235.
[69] M. Coccia, “Varieties of capitalism’s theory of innovation and a concep-
tual integration with leadership-oriented executives: The relation between
typologies of executive, technological and socioeconomic performances,”
Int. J. Public Sector Perform. Manage., vol. 3, no. 2, pp. 148–168, 2017.
[70] M. Coccia, “An introduction to the theories of institutional change,” J.
Econ. Library, vol. 5, no. 4, pp. 337–344, 2018.
[71] M. Coccia, “Artificial intelligence technology in oncology: A new techno-
logical paradigm,” Cornell University, USA. Permanent, 2019. [Online].
Available: http://arxiv.org/abs/1905.06871
[72] M.Pagliaro and M. Coccia, “How self-determination of scholars outclasses
shrinking public research lab budgets, supporting scientific production: A
case study and R&D management implications,” Heliyon, vol. 7, no. 1,
2021, Art. no. e05998.
[73] M. Mosleh, S. Roshani, and M. Coccia, “Scientific laws of research
funding to support citations and diffusion of knowledge in life science,”
Scientometrics, vol. 127, pp. 1931–1951, 2022.
Mario Coccia received the Ph.D. degree in eco-
nomics and commerce from the University of Bari,
Bari, Italy.
He is currently a Research Director with the Na-
tional Research Council of Italy (CNR). He has been
a Visiting Researcher with the Max Planck Insti-
tute of Economics and Visiting Professor with the
Polytechnics of Torino and University of Piemonte
Orientale (Italy). He has conducted research work
in manifold international institutions, such as Yale
University, Georgia Institute of Technology, RAND
Corporation, ASU, UNU-Maastricht Economic and Social Research Institute on
Innovation and Technology (United Nations University-MERIT), University of
Maryland (College Park), Bureau d’Économie Théorique et Appliquée (Stras-
bourg), Munk School of Global Affairs (University of Toronto), and Institute
for Science and Technology Studies (University of Bielefeld). He has authored
or coauthored more than 300 international papers in several disciplines. He
investigates, with interdisciplinary scientific approaches, the determinants of
socioeconomic phenomena of the science and technology, sustainable growth,
and how environment interfaces with human society.
Dr. Coccia is Member of the Editorial Board of manifold international
journals.
Saeed Roshani received the Ph.D. degree in manage-
ment of technology from Allameh Tabataba’i Univer-
sity, Tehran, Iran, in 2019.
He is currently a Research Fellow with Allameh
Tabataba’i University, and the National Research In-
stitute for Science Policy of Iran, Tehran, Iran. He has
authored or coauthored papers published in several
international journals, such as Scientometrics, Tech-
nology Forecasting and Social Change and Sensors.
His research interests include science dynamics and
technological change with methods of mathematical
modelling, machine learning, potentiometric, and agent-based modelling.
Melika Mosleh received the M.S. degree in financial
management from the University of Birmingham,
Birmingham, U.K., in 2020, and the master’s degree
in technology management from the University of
Tehran, Tehran, Iran.
She studied business management with the Uni-
versity of Tehran and scrutinized main topics of tech-
nology and innovation management. She has done
a full scholarship to study her master’s degree. She
was with the Information TechnologyOrganization of
Iran, investigating research policy decision systems
and analyzing startups innovation ecosystem. Her research interests include
advanced mathematics and econometrics, models of machine learning, and
new approaches of text mining. She is currently investigating technological
trajectories of path-breaking innovations and how funding affects the diffusion
of science in society, achieving several publications on international journals
(Scientometrics and Sensors).
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