Analiza-QML-and-QC1

Currently, over 80% of generated digital data is unstructured or semi-structured data. Consequently, identifying patterns and trends, as well as extracting relevant insights from such data, is very challenging. Various data mining techniques and tools can be used to analyze trends and identify new research directions by processing and analyzing thte unstructured data. Using NPL (Natural Language Processing) tools and techniques within a research field or domain ca facilitate text extraction, preprocesing, transformation, feature extraction, pattern recognition, and the grouping of relevant scientific documents (Talib et al. 2016).

Objectivs

The aim of the study is focus on the scientometric analysis of an scientific document dataset containing information on the fields Quantum machine learning (QML) and Quantum Computing (QC) - we use a corpus of scientific documents indexed in the Web of Science database.

THe specific objectives of the research include:

identifying the most cited authors within the network,
analyzing geographical distribution of the scientific publications,
evaluating the evolution of keywords over time

Description of the analyzed dataset

The analyzed dataset comprises of 2119 scientific documents indexed in Web of Science, published between 1999 and 2026. The analyzed documents address various research topics within the fields of QML and QC, and were retrieved via Anelis Plus platform - e-nformation.

Short description of the variables from the analyzed dataset

The analyzed dataset contains 79 variables divided into two types: numerical and non-numerical variables. The table above presents a selection of the most important variables that will be used in this analysis. More details regarding the complete variable descriptions can be found here

In order to obtain the most important bibliometric analysis results, the summary() function will be used. The function provides a tabular summary of essential indicators and descriptive statistics about the dataset, like: the annual volum of scientific publications, the number of citation by author and country, author and country productivity, total citation by country, most relevant scientific publications, most relevant key words etc.

The annual number of scientific documents published

We observe that the highest number of scientific documents was published in 2024 (a total of 506 papers).

The productivity of each author

It is notable that Kim J is the author who published the highest number of articles (20 scientific papers), followed by Park S with 16 scientific documents.

Table. The scientific articles published by PARK S.

Table. The scientific articles published by KIM J.

The scientific activity of Kim J.

We will analyze in detail the scientific activity of Kim J

Each article was published in different scientific journal as:

single author (1 article),
first author (2 articles),
co-author (17 articles, including 2 proceedings paper).

Table. The number of articles written by KIM J as single author is:

Table. The number of articles written by KIM J as first author:

We observe that two articles were written as first author and one paper was written as single author, while the rest were written as co-author.

In generally, the first author is responsible for conducting the majority of the practical work and data analysis. Is the persona that makes the most significant contribution to the research: from defining the objectives and experimental design of the research to writing and editing the final manuscript.

Table. The number of articles in which KIM J is a co-author is:

Table. Type of the published articles

The data reveals that 18 of the articles published by Kim J are standard journal papers, while 2 are conference proceedings papers.

Visual representation of authors collaboration

The representation of co-authorship network centered on Kim J.

Table. The number of the research groups

Table. Composition of the research groups.

In order to evaluate the internal cohesion of each academic group we analyzed the membership composition of the research groups. The above table details the cluster composition, showing the distribution of the authors across identified clusters.

Co-authorship network comprises of 30 authors and 126 connections out of 435 possible links. The network is divided into 7 distinct research groups/clusters. The largest research group is group 1 consisting of 11 members, followed by group 2 with 6 members. We observe that Kim J acts as a bridge, connecting different research groups and individual researchers, being the most influential researcher in the network.

Characteristic of co-authorship network

The adjacency matrix (sociomatrix) is:

##              KIM J PARK S BAEK H JUNG S KIM JP PARK C YUN WJ KIM GS ROH EJ SEOL J CHO S
## KIM J           20     11      5      4      3      3      3      2      2      2     1
## PARK S          11     11      4      4      2      3      2      2      1      0     1
## BAEK H           5      4      5      0      0      0      1      0      1      0     0
## JUNG S           4      4      0      4      2      3      1      0      1      0     1
## KIM JP           3      2      0      2      3      2      2      0      0      0     0
## PARK C           3      3      0      3      2      3      1      0      0      0     1
## YUN WJ           3      2      1      1      2      1      3      0      0      0     0
## KIM GS           2      2      0      0      0      0      0      2      0      0     0
## ROH EJ           2      1      1      1      0      0      0      0      2      0     0
## SEOL J           2      0      0      0      0      0      0      0      0      2     0
## CHO S            1      1      0      1      0      1      0      0      0      0     1
## CHOI J           1      0      0      0      0      0      0      0      0      0     0
## CHOI M           1      1      0      1      0      1      0      0      0      0     1
## CHONG Y          1      0      0      0      0      0      0      0      0      0     0
## CHUNG J          1      1      0      1      0      1      0      0      0      0     1
## HAN Z            1      1      0      0      0      0      0      1      0      0     0
## HONG DW          1      0      0      0      0      0      0      0      0      0     0
## HWANG E          1      0      0      0      0      0      0      0      0      0     0
## JEONG S          1      0      0      0      0      0      0      0      0      0     0
## JHO NS           1      0      0      0      0      0      0      0      0      0     0
## JUNG SY          1      0      0      0      1      0      1      0      0      0     0
## KANCHARLA A      1      0      0      0      0      0      0      0      0      1     0
## KIM D            1      0      1      0      0      0      0      0      1      0     0
## KIM HY           1      0      0      0      0      0      0      0      0      1     0
## KIM JH           1      0      0      0      1      0      1      0      0      0     0
## OH B             1      0      0      0      0      0      0      0      0      0     0
## OH S             1      0      0      0      0      0      0      0      0      0     0
## PARK DK          1      0      0      0      0      0      0      0      0      0     0
## RODRIGUES TK     1      1      0      1      1      1      1      0      0      0     0
## SHIM JY          1      0      0      0      0      0      0      0      0      0     0

The centrality indicators of the co-authorship network centered on Kim J

## 
## 
## Main statistics about the network
## 
##  Size                                  30 
##  Density                               0.193 
##  Transitivity                          0.422 
##  Diameter                              2 
##  Degree Centralization                 0.807 
##  Average path length                   1.807 
##

The author Kim J collaborated with 30 authors (the dimension of the network is 30). The density of the network is 19.3%, which indicates a fragmented macro-structure. The majority of Kim J collaborations were concentrated among Park S, Beak H, and Jung S. Within these scientific communities, the speed of information spreading is fast and clusters frequently forms closed triangles. The co-authorship network is highly centralized because Kim J holds the majority of the connections, while the remaining authors are either isolated or exhibit very fwe collaborations. Consequently, the network is compact, well defined, where most authors are directly connected to the central node, and the remaining participants are a single step away (Newman (2005)).

Visual representation of international collaborations

The universities-level collaboration network

We observe that Kim J is from South Korea and collaborated with researchers from the USA and Japan.

Visual representation of the international collaboration

The institutional level collaboration network

The adjacency matrix for the analyzed research institutions

The composition of the clusters and the centrality indicators of the institutional collaboration network

We observe that institutional collaboration network comprises 5 distinct institutional research groups. The first research group (group 1) consists of 7 reserch institutions, emerging as the largest cluster in the network. The highest betweenness centrality scores are recorded by Korea University, followed by Sookmyung Women’s University and Ajou University. A private corporation also appear within the academic network (specifically, Hyundai Motor Company).

The first group of institutional research group collaborates almost exclusively with Korea institutions. In this case Korea acts as a structure broker (bridge), connecting various research groups across other universities, research institutions, and private corporations. Furthermore, research teams from both Korea University and Sookmyung Women’s University collaborate with reseach institutions form USA Umadevi (2013).

Visual representation of co-citation network (reference co-citation network)

To identify the intellectual structure of the analyzed domain, a reference co-citation network was generated and analyzed.

The reference level representation of co-citation network

Number of citation by each article

The data reveals that the most cited article (with 9697 citation) is the one written by RAISSI M at. al. (titled Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations), and published in J COMPUT PHYS scientific journal in 2019. The paper received 42% more citations than the average score of similar articles published in the same year (2019). Furthermore, the publication average citations per year is 1212 citations (so, the total number of citations is 9697 and we know that the article was written in 2019. The average number of citation per year is 9697/[(2026 - 2019) + 1] = 1212 citation). Given this exceptional citation, this paper seems to be an landmark paper or fundamental study within the analyzed domain. The document has achieved a significant scientific impact in this research field.

Top 10 most cited scientific articles

The title of the article written by researcher Maziar Raissi at al. is

In order to obtain some information about Maziar Raissi we use R function authorBio(). The obtain result is presented below.

## WARNING: No OpenAlex API key detected. Rate limits will be stricter.
## Get a free API key at: https://openalex.org/
## Set it with: Sys.setenv(openalexR_apikey = 'YOUR_API_KEY')
## 
## Retrieving article information for DOI: 10.1016/j.jcp.2018.10.045 
## Article found: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations 
## Total number of authors: 3 
## Authors:
##    1 . Maziar Raissi 
##    2 . Paris Perdikaris 
##    3 . George Em Karniadakis 
## 
## Retrieving information for author at position 1 
## Author name: Maziar Raissi 
## OpenAlex ID: A5012536010 
## Position type: first 
## Is corresponding author: FALSE 
## Waiting 1 seconds before API call...
## 
## === Success ===
## Information successfully retrieved for: Maziar Raissi 
## Number of publications: 93 
## Number of citations: 30190 
## H-index: 30 
## Primary affiliation: Brown University

The author Maziar Raissi, affiliated with Brown University, has published 92 scientific articles. His total number of citation is 30108, with an average number of citations per article of 327 citations.

The analysis reveals that the author has achieved an h-index score of 30, reflecting that 67% of his total published papers have received less than 30 citations each, while the rest of the papers have received at least 30 citations each. Within the competitive fields of QML and QC, an h-index score of 30 is classified as high impact, being associated with full professors at premier research institutions.

Some information about Paris Perdikaris - the second co-author

## WARNING: No OpenAlex API key detected. Rate limits will be stricter.
## Get a free API key at: https://openalex.org/
## Set it with: Sys.setenv(openalexR_apikey = 'YOUR_API_KEY')
## 
## Retrieving article information for DOI: 10.1016/j.jcp.2018.10.045 
## Article found: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations 
## Total number of authors: 3 
## Authors:
##    1 . Maziar Raissi 
##    2 . Paris Perdikaris 
##    3 . George Em Karniadakis 
## 
## Retrieving information for author at position 2 
## Author name: Paris Perdikaris 
## OpenAlex ID: A5002562845 
## Position type: middle 
## Is corresponding author: TRUE 
## Waiting 1 seconds before API call...
## 
## === Success ===
## Information successfully retrieved for: Paris Perdikaris 
## Number of publications: 161 
## Number of citations: 39938 
## H-index: 52 
## Primary affiliation: University of Pennsylvania

Some information about Paris Perdikaris - the third co-author

## WARNING: No OpenAlex API key detected. Rate limits will be stricter.
## Get a free API key at: https://openalex.org/
## Set it with: Sys.setenv(openalexR_apikey = 'YOUR_API_KEY')
## 
## Retrieving article information for DOI: 10.1016/j.jcp.2018.10.045 
## Article found: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations 
## Total number of authors: 3 
## Authors:
##    1 . Maziar Raissi 
##    2 . Paris Perdikaris 
##    3 . George Em Karniadakis 
## 
## Retrieving information for author at position 3 
## Author name: George Em Karniadakis 
## OpenAlex ID: A5009658255 
## Position type: last 
## Is corresponding author: FALSE 
## Waiting 1 seconds before API call...
## 
## === Success ===
## Information successfully retrieved for: George Em Karniadakis 
## Number of publications: 1254 
## Number of citations: 105318 
## H-index: 136 
## Primary affiliation: Brown University

Most productive countries

The significance of each variable is outlined below:

articles - the total number of articles (SCP + MCP)
SCP - single country publication - publications where all authors are affiliated with institutions from the same country (collaboration at the national level)
MCP - multiple country publications - publications where at least one author is affiliated with institutions from different countries (collaboration at international level)
frequency - proportion of articles
MCP_Ratio - the proportion of articles written by authors who collaborate at the international level

Tabel. Top 10 most productive countries between 1999 and 2026.

Publications are classified into two categories: those authored by researchers from the same country (domestic collaborations) and those involving co-authors from different countries (international collaborations). The table above presents the empirical values obtained for these collaboration metrics.

The number of total citations by countries

Relevant scientific journals

Most relevant keywords

The majority of the articles are written by the authors or researchers from Computer Science field (399 scientific articles), followed by those from Physics domain (328 scientific papers). In the figure above is presented the wordcloud of scientific domain.

Distribution of papers by contributing research domain between 2011 and 2026 It can be observed that while the number of research areas contributing to the development of the QML and QC fields was initially limited, a significant expansion occurred after 2019, with publications emerging from a diverse range of disciplines. The period prior to 2019 was heavily dominated by research affiliated with fields such as Physics and Computer Science. However, post-2019, the domain experienced an influx of publications from other scientific disciplines, each providing distinct contributions to the advancement of the field.(Bansal and Rajput 2025).

Conclusions

This study presents a bibliometric analysis of the Quantum Computing and Quantum Machine Learning fields, based on scientific documents published between 1999 and 2026 and retrieved from Web of Science. Although the advancement of the analyzed domains has been significant, the volume of scholarly literature in this area remains relatively small, comprising a corpus of 2119 scientific documents. The bibliometric analysis was performed using the R package bibliometrix. In this study we evaluate the main descriptive characteristics of the publications, such as: annual volume of scientific documents, author productivity, country scientific production, citation counts by both author and country, total citations per country, as well as the most relevant scientific publications and keywords etc. The obtained results indicate that the vast majority of publications emerged after 2019, reflecting an expansion of research interest in the analyzed fields. The USA remains the most productive country, followed by China and India. Furthermore, the USA leads in terms of single country publications (SCP or domestic research), whereas China accounts for the highest volume of multiple country publications (MCP or international collaboration). Combining the capabilities of quantum computing with classical machine learning can accelerate advancement across various domains, such as healthcare and materials science etc.

Bibliography

Martin Geissmann, Comparison of Word Cloud R Packages, 2024, https://rpubs.com/mgei/1259234 accessed on 03.07.2026.

Scientometric analysis of the QML and QC fields

by Mihaela Irimia, Date: 2026-07-01