1 Introduction
Research strength analysis refers to measuring, comparing, and analyzing the research status of different scientific research bodies (such as countries, institutions, researchers, et al.) in various research fields (Ma et al., 2018). Bibliometrics is commonly recognized as an efficient approach for measuring, comparing, and assessing the performance/strength of scientists, institutions, and countries (Díaz-Faes et al., 2015; Haeffner-Cavaillon & Graillot-Gak, 2009; Harnad, 2008; Inglesi-Lotz & Pouris, 2011; Jia et al., 2014). The number of papers and citations are most commonly used as the indicators (Liu & Mei, 2015; Mokhnacheva & Kharybina, 2011; Morris et al., 2003; Shibata et al., 2008; Small et al., 2014; Small & Upham, 2009). However, assessing scientific strength should be more constructive under the background of seeking self-reliance and self-strengthening. Hence, the paper provides a novel model synthesizing the national scientific self-reliance and the national academic contribution.
The measure of scientific self-reliance and allocation of academic contribution is essential for national research strength to assess in this paper, and there are many ways to measure these two indicators. In this paper, scientific self-reliance refers to the rate of independent publications and the degree of research autonomy in collaboration based on the international collaboration patterns (Edler, 2010; González-Alcaide et al., 2017; Kato & Ando, 2017; Zheng et al., 2014; Zou & Laubichler, 2017). The previous studies on international collaboration are measured mainly through various indicators, such as the number, share, and intensity from different perspectives (Chen et al., 2019). However, previous studies only took into account the number of papers published by the country as corresponding or first author in international collaboration (Cho et al., 2010; Egghe, 1991), when they calculated the dominance degree of a country, resulting in ignoring the dominance of the country in other collaboration positions. Thus, in this paper, we propose five collaboration dominance patterns based on the different academic positions of countries to measure the degree of national scientific self-reliance in research collaboration. Allocation of academic contribution is also essential for national scientific research strength to assess, and it is one of the factors we consider in building the metric model. Various methods have been proposed for calculating academic contributions. The earliest method was the First Author Counting proposed by Cole & Cole (1974), which only considered the contribution of the first author and ignored the contribution of other authors. Lindsey (1980) used the Normal Counting method, which allocated the same contribution weight to each author, resulting in magnifying the secondary authors' contributions and is unfair to the primary authors. Besides, there are methods based on the order of authorship, mainly including Fractional Counting (Charles & Oppenheim, 1998), Proportional Counting (Abbas, 2010, 2011; Van Hooydonk, 1997), Geometric Counting (Egghe et al., 2000), Harmonic Counting (Hagen, 2010; Hodge et al., 1981), Combined Credit Allocation (Liu & Fang, 2012a, 2012b), Correct Credit Distribution (Lukovits et al., 1995), and Network-based Allocation (Kim & Diesner, 2014). This method is a significant improvement over the Normal Counting (Lindsey, 1980), taking into account the effect of the number of authors and the rank of the byline on the size of the contribution. It is worth noting that the Network-based Allocation can reorder co-author sequences. If several corresponding authors are in a co-author sequence, then the related authors can be reordered based on the magnitude of their contributions before the contribution assignment. Based on the advantages of the Network-based Allocation, we calculate the national academic contribution based on the author's signature position and the contribution transfer principle in designing the national research strength metric model.
Considering the above model indicators, we explore a metric model for national scientific research strength evaluation through cooperation on research papers. The model mainly includes two indicators, national scientific self-reliance (SR) and national academic contribution (CT), to reflect “self-reliance” and “self-strengthening”, respectively. The measure of these two indicators takes into account the author's signature position and the citation frequency of the paper. The metric model is applied in evaluating China's quantum research strength.
The rest of the paper is organized as follows. In Section 2, the data collection and methods used in this paper are described. In Section 3, we present the specific experimental process and detailed results. Finally, we conclude the paper in Section 4.
2 Methodology and Data
2.1 National strength in scientific research
From the perspective of scientific research output, national strength in scientific research for a country could be regarded as the country's scientific contribution to the world. Considering the contribution difference made by co-authors from different countries at the paper level, this metric model sets two indicators to access the national strength in scientific research for country i (SSi): a. the national contribution to academic impact (CTi), b. the national scientific self-reliance for a country (SRi). The metric model of national strength in scientific research is designed as follows:
SSi = CTi * SRi
Where SSi is the scientific research strength index of country i, CTi is the academic contribution of country i, SRi is the national scientific self-reliance index of country i.
2.2 National contribution to academic impact
The contribution distribution of each author in multi-author papers is complicated, and there is no unified method for it. However, only considering the contribution of the first author, corresponding author, or the average distribution is unfair. Since the author with the higher signature position in a paper makes more academic contributions (the corresponding author is placed in the first place in the calculation process). The author contribution transfer factor “d” is designed, which can be used to determine the academic contribution transferred by the author with the lower signature position to the author with the higher signature position in a paper. When calculating the author's academic contribution to the paper, the academic contribution of the paper is evenly distributed to each collaborator, and then the author with the lower signature position forwards part of his academic contribution to the author with the higher signature position in turn. The size of the academic contribution transferred is determined by the author's contribution transfer factor “d”. Additionally, the cited frequency is used for measuring the academic contribution of a paper with multi-authors. The measure of the country's academic contribution (CT) is as follows:
$C{{T}_{i}}=\sum\limits_{m\in {{m}_{i}}}{\left[ \frac{V}{M}+\frac{V}{M}*d*\left( \alpha \sum\limits_{n=1}^{M-m}{\frac{1}{M-n}-\beta } \right) \right]}$
Where V is the cited frequency of the paper (V ≥ 1). M is the number of authors of the paper. m is the order of authorship (1 ≤ m ≤ M), mi is a set of the order of authorship belonging to country i. d is the author contribution transfer factor (d = 0.5). $\alpha $ is the contribution benefit coefficient ($\alpha $ = 1), $\beta $ is the contribution loss coefficient ($\beta $ = 1). It should be noted that if the author is in the first position (the first author or the corresponding author), there will be no contribution loss for the author, then $\beta $ = 0. If the author is in the last position, there will be no contribution gain for the author, then $\alpha $ = 0.
2.3 National scientific self-reliance
The national scientific self-reliance (SR) for a country shows the autonomy intensity in research, which can be reflected by the complete independence in the paper produced by a country and the national autonomy in the multi-countries paper. Based on this principle, this paper designs the national scientific self-reliance index (SR) to more comprehensively consider the scientific research dominant degree of a country in a certain field.
$S{{R}_{i}}=\frac{N_{i}^{t}}{S_{i}^{t}}\sum\limits_{j\in Cor{{p}_{t}}}{\left( \frac{N_{ij}^{t}}{N_{i}^{t}}*Autonom{{y}_{i\to j}} \right)+\left( 1-\frac{N_{i}^{t}}{S_{i}^{t}} \right)}*Autonom{{y}_{indep}}$
where $N_{i}^{t}$ is the total number of cooperative papers produced by country i with other countries at time t, $S_{i}^{t}$ is the total number of papers produced by country i at time t. Corpi is the set of cooperating countries for country i. $N_{ij}^{t}$ is the number of cooperative papers of countries i and j at time t.
For the national scientific self-reliance shown by the country's independent publications, this paper calculates the proportion of independent papers published by country i to all papers published by country i in this field. As shown on the right side of the plus sign in equation 3, where $\left( 1-\frac{N_{i}^{t}}{S_{i}^{t}} \right)$ is the proportion of independently published papers in the country i, Autonomyindep is the research autonomy index demonstrated by the independent publication of country i, and its value is 1.
For the national scientific self-reliance shown by the country collaborated with other countries, we first calculate the proportion of the multi-countries papers published by country i to all papers published by country i, and then calculate the sum of scientific research autonomy between the country i and all its collaborated countries, which are referred as “j” in equation 3, and finally multiply the two values. As shown on the left side of the plus sign in equation 3, where $\frac{N_{i}^{t}}{S_{i}^{t}}$ is the proportion of multi-countries papers published by country i, Autonomyi→j is the research autonomy index of country i in research collaboration between countries i and j. $\sum\limits_{j\in Cor{{p}_{t}}}{\left( \frac{N_{ij}^{t}}{N_{i}^{t}}*Autonom{{y}_{i\to j}} \right)}$ is the sum of the scientific research autonomy of country i to each country j in cooperation.
The autonomy we consider here is based on collaboration between two countries. For example, to the cooperative countries, country i and country j, the national autonomy of country i (Autonomyi→j) is calculated by subtracting the dominant degree of country j ($Dominant_{j\to i}^{t}$) from the dominant degree of country i ($Dominant_{i\to j}^{t}$). The calculation method is as follows:
$Autonom{{y}_{i\to j}}\text{=}Dominant_{i\to j}^{t}-Dominant_{j\to i}^{t}$
Where the research autonomy index (Autonomyi→j) takes values in the range (-1,1), if Autonomyi→j ≤ 0, then country i has no research autonomy with country j. if Autonomyi→j > 0, country i exists research autonomy with country j. The closer the value of the research autonomy index is to 1, the stronger the research autonomy of country i in research collaboration.
In previous studies, when calculating the dominant degree of country i over country j, the number of papers in which country i was the corresponding or first author during the collaboration was counted (Cho et al., 2010; Egghe, 1991). Here, the concept of cooperative position is introduced to assess the national dominant degree of a country. Firstly, all the participant countries are divided into three types according to the signature position. (1) The dominant country plays a leading role in a paper and is decided by the corresponding author and the first author. Generally, the corresponding author is the leader of the research project and responsible for the design, organization, and planning, and the first author is the main writer of the paper. They are both the dominator of the paper. (2) The largest contribution country is decided by the national contribution to academic impact (CTi) based on the principle of contribution transfer. Although the corresponding author and the first author dominate a paper, other collaborators' contributions should be accounted. (3) The subordinate country is the cooperative country which is neither dominant nor the largest contributor (Wang, 2014). Secondly, any two cooperative countries, such as country i and country j could be located in the different positions in Table 1 , and to country i, it exists five collaboration dominance patterns (Strongly dominant, Substrongly dominant, Dominant, Subweakly dominant, Weakly dominant), five different weights are assigned respectively to calculate the dominant degree of country i to country j ($Dominant_{i\to j}^{t}$). The sum of the five weights wk is 1, and their values are equidistantly decreasing in order, that is, 5/15, 4/15, 3/15, 2/15, 1/15 respectively.
Table 1. Five dominance patterns of Dominanti→j. |
| Collaboration patterns | Dominant country | Largest contributing country | Subordinate country | Weight |
|---|---|---|---|---|
| Strongly dominant | i | i | j | 5/15 |
| Substrongly dominant | i | j | 4/15 | |
| Dominant | i | j | 3/15 | |
| Subweakly dominant | i | j | 2/15 | |
| Weakly dominant | i j | 1/15 |
$Dominant_{i\to j}^{t}=\frac{\sum\nolimits_{k=1}^{5}{N_{{{k}_{i\to j}}}^{t}{{W}_{k}}}}{N_{ij}^{t}}$
where $N_{{{k}_{i\to j}}}^{t}$ is the number of cooperative papers of country i and country j at time t in collaboration pattern k with the weight (wk). $N_{ij}^{t}$ is the total number of collaborative papers of country i and country j at time t. The greater $Dominant_{i\to j}^{t}$ indicates, the stronger the leading role played by country i to country j at time t.
2.4 Data Source
The data used for this method was collected from the Web of Science (WoS) database. We utilize the following search strategy (Zhang et al., 2018) for quantum technology papers which is based on the website of qurope.eu (BINOSI & CALARCO, 2017): TS=((“Quantum” and ((“information”) OR (“eraser”) OR (“Quantum Classical Transition”) OR (“coherence”) OR (“entanglement”) OR (“measurement”) OR (“network”) OR (“storage”) OR (“memory”) OR (“communication”) OR (“fingerprint”) OR (“processor”) OR (“Cavity QED”) OR (“clock synchronization”) OR (“image”) OR (“sensor”) OR (“magnetometry”))) OR ((quantum NEAR/5 comput*) OR (quantum NEAR/15 algorithm*) OR (quantum NEAR/10 simulat*) OR (quantum NEAR/10 error*) OR (“quantum circuit” OR “Quantum cellular automata” OR “Quantum Turing machine” OR “quantum register”) OR (quantum NEAR/10 communication*) OR (quantum NEAR/15 protocol*) OR (quantum NEAR/15 cryptograph*) OR (“quantum key”))).
We retrieved and downloaded paper data (Article and Review) from 1990 to 2021 in the WoS database for the bibliometric analysis (as of July 2021). Then We performed data cleaning, including removing duplicates and data with missing C1 fields. Finally, we collected a total of 175,002 publication records published by 147 countries. Each record has 30 meta-data fields: authors, title, affiliation, abstract, keywords, publication source, and reference list. All data processing, calculation, and exploration were conducted via python scripts.
3 Results
3.1 China's position in the global collaboration network in quantum technology
The United States (US) and China are the top two countries based on the number of papers published in quantum technology, followed by Germany and England. There are 147 countries that publish 175,002 quantum technology papers, and 75.69% of the total papers are posted by the top 10 countries with the highest publications (see Table 2 (a)). There are 40,180 papers are from China, accounting for 22.96% of 175,002 papers, and 24.57% of them are published by multi-countries. The international collaboration rate is the lowest compared to the top 10 highly productive countries in quantum technology research, and the majority (10.58%) collaborated with the US (see Table 2 (b)). Compared with European countries, especially Germany, England, and France, Asian countries, such as China, India, and Japan, are more independent with lower collaboration rates (in this case, 24.57%, 30.82%, and 39.85%, respectively).
Table 2. Top 10 countries with the highest number of papers in quantum technology (a) and China's research collaboration layout (b). |
 |
Note: aCollaboration strength is calculated with Salton formula (Salton, 1983) |
The development stage of quantum technology is manifested in the logistic growth curve by fitting the accumulation of literature. There is a goodness of fit with R2 = 0.919, and the model can effectively predict the development stage of quantum technology research (see Fig. 1 ). At present, the exponential growth period has just ended, and the number of papers will still increase. What's more, the model also presents the degree of quantum technology maturity and its corresponding time, that is, 0.1 (2003), 0.5 (2018), 0.9 (2034), and 0.99 (2049). China's paper amount surpassed the US's in 2013 and surpassed Europe's in 2020. China has been a big nation with the most significant number of papers and shows a continued growth trend in quantum technology research.
Figure 1. The growth trend of papers of quantum technology by China, USA, and Europe.Note: The dotted line without dots is the predicted value in the cumulative growth curve. |
Cooperation in scientific research is essential for a country to participate in global development. A country's position in the global cooperation network can reflect its own scientific and technological strength, and reflect its dominant power in future scientific and technological development. In this study, we construct a network of national scientific collaboration in the field of quantum technology (see Fig. 2 ). The strength of collaboration between countries along the Belt and Road, such as Sri Lanka, Cyprus, Georgia, Estonia, and Egypt, is the highest in the international research collaboration network. Although the number of collaborations among these countries is minimal, the strength of collaboration is among the top globally (see Table 3 ). The US and European countries emphasize international collaboration, but most are European countries. China is more independent in quantum research, with a large proportion of papers on its own. There are only 9,817 multi-nations papers collaborated with 99 countries in China's 40,180 quantum research papers. Most cooperation partners come from developed countries, such as the US, Singapore, Germany, England, et al. (see Table 2 (b)).
Figure 2. Research collaboration strength network in the field of quantum technology.Note: The nodes represent countries that have published papers in quantum technology. The edges represent the scientific collaboration between countries. The weights of the edges represent the strength of collaboration between countries calculated by the Salton formula (Salton, 1983). The node size represents the size of the betweenness centrality of a country, and the larger the node, the more collaboration resources the country controls. The thickness of the lines represents the collaboration strength, and the thicker the lines, the stronger the collaboration strength between the two countries. We selected 53 countries based on their collaboration strength (> 0.06). |
Table 3. Top 5 collaboration countries with the highest collaboration strength in quantum technology. |
| No. | Collaboration country (Number of papers) | Collaboration strengtha | Collaboration papers |
|---|---|---|---|
| 1 | Sri Lanka (64); Cyprus (109) | 0.51 | 43 |
| 2 | Sri Lanka (64); Georgia (139) | 0.46 | 43 |
| 3 | Estonia (189); Sri Lanka (64) | 0.39 | 43 |
| 4 | Cyprus (109); Georgia (139) | 0.38 | 47 |
| 5 | Egypt (1,386); Saudi Arabia (1,567) | 0.36 | 528 |
Note: aCollaboration strength is calculated with Salton formula (Salton, 1983) |
Global quantum research is dominated by the US and Europe (i.e. England, France, Germany) with high betweenness centrality, which refers to the ability to control information resources in a network (Brandes, 2001). By contrast, China's network centrality indexes are lower, betweenness ranked 6th, degree ranked 5th, and Closeness ranked 5th, well below the 2nd ranking by papers amount (see Table 4 ).
Table 4. Statistics of the network centrality for the top 10 countries with the highest betweenness centrality in quantum technology. |
| No. | Country | Betweenness Centrality | Degree Centrality | Closeness Centrality |
|---|---|---|---|---|
| 1 | France | 0.0700 | 106 | 0.7650 |
| 2 | South Africa | 0.0607 | 90 | 0.7083 |
| 3 | USA | 0.0594 | 111 | 0.7846 |
| 4 | Germany | 0.0518 | 106 | 0.7650 |
| 5 | Spain | 0.0516 | 94 | 0.7183 |
| 6 | China | 0.0427 | 99 | 0.7391 |
| 7 | England | 0.0421 | 105 | 0.7612 |
| 8 | India | 0.0384 | 94 | 0.7217 |
| 9 | Canada | 0.0367 | 92 | 0.7116 |
| 10 | Sweden | 0.0335 | 89 | 0.7018 |
3.2 China's academic contribution in quantum technology
Based on the proposed indicator CTi (see Equation 2), China is the second-largest contributor to quantum technology, accounting for 12.6% of the whole world's contribution, and is the unique developing country ranked in the top 10 countries (see Table 5 ). Besides, although the US's total contribution proportion (i.e. 30.57%, see Table 6 ) is much higher than China's, it presents a decreasing trend year by year (see Fig. 3 left), from 38.08% in 2001 to 17.82% in 2020. By contrast, China's contribution proportion significantly increased from 3.25% in 2001 to 27.81% in 2020 (see Fig. 3 right), much higher than that of the US in 2020. The same trend is also observed in the total contribution proportion of developed countries vs. developing countries. It is worth noting that the proportion of papers with zero citation in developing countries is much higher than that in developed countries, for example, 5.44% in USA, 4.01% in Germany and 3.70% in England, by contrast, 12.14% in China, 12.25% in India and 11.53% in Russia. (cf., Appendix 1 )
Table 5. Ranking of academic contribution (CT) in global quantum technology. |
| No. | Country | CT | Contribution proportion | No. | Country | CT | Contribution proportion |
|---|---|---|---|---|---|---|---|
| 1 | USA | 1,593,667.96 | 30.57% | 75 | Cameroon | 364.35 | 0.007% |
| 2 | China | 639,792.41 | 12.28% | 76 | Iceland | 358.65 | 0.007% |
| 3 | Germany | 471,644.89 | 9.05% | 77 | Moldova | 332.54 | 0.006% |
| 4 | England | 317,155.23 | 6.08% | 78 | Indonesia | 326.91 | 0.006% |
| 5 | Japan | 230,317.08 | 4.42% | 79 | Ethiopia | 294.08 | 0.006% |
| 6 | Italy | 199,203.76 | 3.82% | 80 | Philippines | 291.82 | 0.006% |
| 7 | France | 198,179.40 | 3.80% | 81 | Czechoslovakia | 281.92 | 0.005% |
| 8 | Canada | 163,038.66 | 3.13% | 82 | Kazakhstan | 238.84 | 0.005% |
| 9 | Austria | 154,559.69 | 2.96% | 83 | Jordan | 213.80 | 0.004% |
| 10 | Switzerland | 135,561.92 | 2.60% | 84 | Kuwait | 206.25 | 0.004% |
| 11 | Spain | 113,040.28 | 2.17% | 85 | Sri Lanka | 200.63 | 0.004% |
| 12 | Australia | 111,733.35 | 2.14% | 86 | Oman | 196.78 | 0.004% |
| 13 | India | 91,204.80 | 1.75% | 87 | Lebanon | 162.98 | 0.003% |
| 14 | Netherlands | 80,271.91 | 1.54% | 88 | Malta | 155.93 | 0.003% |
| 15 | South Korea | 62,339.05 | 1.20% | 89 | Brunei | 98.70 | 0.002% |
| 16 | Russia | 61,630.01 | 1.18% | 90 | Azerbaijan | 92.67 | 0.002% |
| 17 | Israel | 60,244.46 | 1.16% | 91 | Palestine | 83.25 | 0.002% |
| 18 | Poland | 51,529.10 | 0.99% | 92 | Macedonia | 81.75 | 0.002% |
| 19 | Sweden | 46,708.93 | 0.90% | 93 | Vatican | 74.46 | 0.001% |
| 20 | Brazil | 41,762.49 | 0.80% | 94 | Bosnia & Herceg | 72.07 | 0.001% |
| ... | ... | ... | ... | ... | ... | ... | ... |
| 74 | Bahrain | 368.82 | 0.007% | 147 | Eritrea | 0.23 | 0.000004% |
Note: Developing countries in gray background. The basis for the division between developed and developing countries is the Word Economic Outlook(International Monetary Fund, 2018), in which International Monetary Fund (IMF) divides 193 countries into two categories: 39 developed countries and 154 developing countries. |
Table 6. Partial results of the research autonomy in national research collaboration (ranking by China's collaboration strength) |
| China | USA | Singapore | Japan | Australia | ... | Algeria | |
|---|---|---|---|---|---|---|---|
| China | ↙10.36% ↑-9.66% | ↙10.66% ↑-9.05% | ↙11.76% ↑-5.10% | ↙9.53% ↑-10.84% | ↙6.67% ↑0 | ||
| USA | ↙20.02% ↑9.66% | ↙12.97% ↑0.09% | ↙12.92% ↑-1.58% | ↙14.18% ↑0.91% | ↙12.38% ↑1.90% | ||
| Singapore | ↙19.71% ↑9.05% | ↙12.88% ↑-0.09% | ↙15.87% ↑5.333% | ↙15.22% ↑4.03% | ↙0.00% ↑0 | ||
| Japan | ↙16.86% ↑5.10% | ↙14.51% ↑1.58% | ↙10.54% ↑-5.33% | ↙15.79% ↑5.53% | ↙33.33% ↑33.33% | ||
| Australia | ↙20.37% ↑10.84% | ↙13.28% ↑-0.91% | ↙11.19% ↑-4.03% | ↙10.26% ↑-5.53% | ↙0.00% ↑-33.33% | ||
| ... | ... | ... | |||||
| Algeria | ↙6.67% ↑0 | ↙10.48% ↑-1.90% | ↙0.00% ↑0 | ↙0.00% ↑-33.33% | ↙33.33% ↑33.33% | ... |
Notes: ↙represents the $Dominant_{i\to j}^{t}$ (see Equation 5) for the dominance of country i (column label) over the country j (row label); ↑represents the Autonomyi→j (see Equation 4) for measuring the dominance difference between country i (column label) and country j (row label), the positive value represents the dominance of country i is higher than country j, and the negative value represents the opposite results. |
Figure 3. Changes in the contribution of China and the US in developed and developing countries.Note: The first column on the left represents the developed countries' contribution proportion from 2001 to 2020. The second column on the left represents the USA's contribution proportion from 2001 to 2020. The first column on the right represents the developing countries' contribution proportion from 2001 to 2020. The second column on the right represents China's contribution proportion from 2001 to 2020. |
Appendix 1. The fundamental statistic of publications of zero citations. |
| Country | Number of Papers | Zero citation Papers | Proportion |
|---|---|---|---|
| USA | 40,906 | 2,224 | 5.44% |
| Peoples R China | 40,180 | 4,876 | 12.14% |
| Germany | 18,633 | 748 | 4.01% |
| England | 11,904 | 441 | 3.70% |
| Japan | 11,726 | 958 | 8.17% |
| Italy | 8,937 | 492 | 5.51% |
| India | 7,394 | 906 | 12.25% |
| Russia | 6,252 | 721 | 11.53% |
| Brazil | 3,520 | 316 | 8.98% |
| Iran | 3,061 | 427 | 13.95% |
Note: In the table the top five developed countries and the top five developing countries with the highest number of papers are selected, by which the number of papers published is 152,513, accounting for 87.15% of the total number of papers 175,002. |
CT see Equation 2 in Section 2.
$\text{Contribution Proportio}{{\text{n}}_{i}}=C{{T}_{i}}/Total\text{ CT}$
3.3 China's research autonomy in quantum scientific collaboration
In this section, we try to understand China's research autonomy in quantum scientific collaboration through the research autonomy index (Autonomyi→j) (see Equation 4) (see Table 6 ).
As shown in Table 6 , China's dominance over the US is 20.02%, while the US's dominance over China is 10.36%. Thus the research autonomy index for China over the US (AutonomyChina→US) is 9.66%, indicating that China has research autonomy in Sino-US research collaboration. Overall, among the 31 developed countries cooperating with China, 28 countries have lower dominance than China, only two countries (i.e. Iceland and New Zealand) have higher dominance, and one country (Malta) has the same dominance as China (see Table 7 ). Among 68 developing countries cooperating with China, the corresponding number of countries is 42, 11, and 15 respectively. The results show that China plays a leading role in international collaboration in quantum technology, whether the collaboration countries are developed or developing countries.
Table 7. Distribution of the number of countries with AutonomyChina→countries. |
| AutonomyChina→countries > 0 | AutonomyChina→countries < 0 | AutonomyChina→countries = 0 | |
|---|---|---|---|
| Developed countries (31) | 28 | 2 | 1 |
| Developing countries (68) | 42 | 11 | 15 |
Note: In the row label, (31) and (68), represents the number of developed and developing countries in our datasets respectively. AutonomyChina→countries represents the dominance difference between China and developed/developing countries. |
The distribution of the proportion of papers in five dominance patterns for China-leading research collaboration in quantum technology is listed in Table 8 . We found that China often plays a role as the dominant country (the first row in Table 8 ), and the largest contribution country when collaborating with the developed countries. In particular, China mainly cooperates as the strongly dominant type with the US, Germany, England, and Japan. By contrast, as the weak dominant type with the developing countries (the 9th row in Table 8 ). We explain the results as, developed countries have strong research strength in quantum technology, and China is more active in the cooperation with developed countries. Therefore, China often prefers to lead the cooperation with developed countries. However, the weak research strength of developing countries, China's cooperation attitude with developing countries in this field is relatively negative and China often participates together with the developing country as the subordinate country in the collaboration dominated by other countries.
Table 8. Distribution of the proportion of papers in the five dominance patterns of DominantChina→countries. |
| China | Strongly dominant | Substrongly dominant | Dominant | Subweakly dominant | Weakly dominant |
|---|---|---|---|---|---|
| Developed Countries | 64.13% | 1.64% | 1.01% | 1.26% | 31.96% |
| USA | 79.99% | 2.39% | 0.65% | 1.30% | 15.66% |
| Germany | 66.77% | 0.81% | 1.21% | 0.70% | 30.51% |
| England | 63.17% | 1.02% | 1.89% | 0.87% | 33.04% |
| Japan | 67.23% | 1.38% | 0.61% | 2.60% | 28.18% |
| France | 41.99% | 1.10% | 1.38% | 1.10% | 54.42% |
| Italy | 49.40% | 5.22% | 0.80% | 2.01% | 42.57% |
| Canada | 69.73% | 1.44% | 1.26% | 1.08% | 26.49% |
| Developing Countries | 29.75% | 0.51% | 1.06% | 1.24% | 67.44% |
| India | 42.52% | 2.80% | 1.40% | 2.34% | 50.93% |
| Russia | 31.58% | 0.38% | 1.88% | 0.75% | 65.41% |
Note: The five dominance patterns are classified based on DominantChina→countries represents China's dominance in scientific research cooperation with developed/developing countries. The countries are selected based on the number of their papers published in quantum technology (see |
3.4 China's national strength in quantum scientific research
China's SS value is second only to the United States according to equation 1 (see Table 9 ), indicating that the US and China have become the most prominent countries in quantum technology. There are 12 developed countries vs. 3 developing countries (China, India, and Russia) ranked among the top 10% with highly SS. With the exception of China, India, and Russia, most developing countries are weaker in scientific research strength. The national scientific self-reliance (SR) for a country shows the autonomy intensity in research, which can be reflected by the complete independence in the paper produced by a country and the national autonomy in the multi-countries paper. Therefore, China's high SR is caused by the high proportion of independent publications and high autonomy in research cooperation. And the similar result is also observed in India's SR, as seen in Table 1 , where the proportion of research collaboration is only 30.82%. However, high SR does not indicate high SS, for example, India has high SR but low SS and the US has low SR but high SS, the same can be applied to Germany and the UK. While China is special with both high SR and SS.
Table 9. Ranking of scientific research strength index (SS) in global quantum technology. |
| No. | Country | SR | SS | No. | Country | SR | SS |
|---|---|---|---|---|---|---|---|
| 1 | USA | 0.54 | 853,088.21 | 75 | Philippines | 0.22 | 63.31 |
| 2 | China | 0.77 | 493,650.57 | 76 | Moldova | 0.19 | 61.86 |
| 3 | Germany | 0.36 | 170,519.88 | 77 | Indonesia | 0.16 | 51.88 |
| 4 | Japan | 0.59 | 136,364.59 | 78 | Macedonia | 0.62 | 50.78 |
| 5 | England | 0.33 | 105,841.36 | 79 | Kazakhstan | 0.21 | 49.26 |
| 6 | Italy | 0.42 | 84,291.22 | 80 | Jordan | 0.21 | 45.08 |
| 7 | India | 0.70 | 63,615.28 | 81 | Cuba | 0.07 | 41.72 |
| 8 | France | 0.32 | 63,100.22 | 82 | Qatar | 0.03 | 35.43 |
| 9 | Canada | 0.34 | 54,791.26 | 83 | Jamaica | 0.61 | 34.89 |
| 10 | Austria | 0.28 | 43,443.24 | 84 | Serbia Monteneg | 0.53 | 30.53 |
| 11 | Switzerland | 0.28 | 37,720.08 | 85 | Bahrain | 0.08 | 29.09 |
| 12 | Australia | 0.33 | 36,955.01 | 86 | Oman | 0.14 | 27.10 |
| 13 | Spain | 0.31 | 34,742.01 | 87 | Sri Lanka | 0.12 | 24.12 |
| 14 | South Korea | 0.55 | 34,124.41 | 88 | Brunei | 0.24 | 23.50 |
| 15 | Russia | 0.46 | 28,491.90 | 89 | North Korea | 0.33 | 23.45 |
| 16 | Iran | 0.77 | 23,826.65 | 90 | Malta | 0.14 | 21.40 |
| 17 | Israel | 0.37 | 22,480.51 | 91 | North Macedonia | 0.29 | 19.60 |
| 18 | Netherlands | 0.27 | 21,887.75 | 92 | Lebanon | 0.10 | 15.97 |
| 19 | Brazil | 0.52 | 21,704.77 | 93 | Bosnia & Herceg | 0.15 | 11.01 |
| 20 | Poland | 0.41 | 20,901.86 | 94 | Azerbaijan | 0.10 | 9.32 |
| … | … | … | … | … | … | … | … |
| 74 | Cyprus | 0.08 | 29.09 | 147 | Panama | -0.08 | -5.01 |
Note: Developing countries in gray background SR see Equation 3 in Section 2 SS see Equation 1 in Section 2 |
The national scientific self-reliance index (SRi) trends for the top five developed countries and the top five developing countries with highly SS are shown in Fig. 4 . Overall, the values of SR of the five developed countries (i.e. USA, Germany, Japan, England, Italy) all show declining trends, but their relative positions remain unchanged (Fig. 4 left). The values of SR of the US and Japan are higher than the other three European countries, Germany, England, and Italy. The developing countries, except Brazil, all show a slowly increasing or steady trend (Fig. 4 right). In particular, China kept the highest value of SR over time, and Iran's SR increased significantly and caught up with China in 2006. Brazil's SR began to decline significantly after 2011, and then it remained flat with Russia. It shows that the proportion of developed countries published independently in quantum technology and the research autonomy in scientific collaboration is constantly decreasing. The proportion of developing countries, especially Iran, independently published papers in quantum technology, and their research autonomy in scientific collaboration has been dramatically improved. Although China's scientific self-reliance index in quantum technology has risen slightly, it is relatively stable. China has always maintained high independence in the development process of quantum technology.
Figure 4. The time trend of national scientific self-reliance index (SR). |
Figure 5. The time trend of national rankings based on scientific research strength index (SS). |
Besides, the position of the other three developing countries, India, Russia, and Iran, in global quantum technology is also continuously rising and has been in the top 10 SS rankings in 2020. Especially Iran, which has risen from 61st in 2001 to 4th in 2020, having taken a significant position in driving quantum technology development. The results indicate that while developed countries have strong scientific research strength in the quantum field, some developing countries have shown increasing contribution to this area, and scientific autonomy, as well as scientific strength.
4 Conclusions
This paper explores a metric model for assessing national strength in scientific research to understand China's research output in quantum technology through collaboration. To this end, we propose two indicators from two perspectives: the national contribution to academic impact and the scientific self-reliance, to measure and assess China's scientific research strength and make a comparison with the US and other outstanding countries in global quantum technology, such as Germany, England, Japan, and Italy in developed countries and Russia, India, Iran, and Brazil in developing countries.
Our results lend support to China's prominent position in quantum technology currently (Smith-Goodson, 2019) measured by the metric model of national strength in scientific research. The proportion of international collaboration papers of China is lower and the research on quantum technology in China locates in a more marginal position in global cooperation networks. However, China's total contribution to quantum technology is ranked the world 2nd, and its annual contribution has surpassed the US since 2015. The gradually increasing advantage for China vs. USA is also witnessed in Fig. 3 , measured by the indicator national academic contribution (CT). What's more, China shows a higher scientific autonomy in international collaboration measured by the research autonomy indicator (Autonomyi→j) and exhibits different dominant patterns: Strongly dominant type is found when China dominates the research collaboration with developed countries, especially with the US, Germany, England, Japan, and Canada; While weakly dominant type is found when China dominates the research collaboration with developing countries. It's an interesting result and more data are needed to explore the reason behind it in further research, for instance, the relationship between the results and Journal Impact Factor or citations.
China's scientific self-reliance is gradually increasing (see Fig. 4 right) and its scientific strength in quantum technology has surpassed the US, and taken a world prominent position (see Fig. 5 ). Some other developing countries, such as India, Russia, and Iran, which have also recognized the strategic importance of quantum technology and continue making more efforts in this area (Fedorov et al., 2019; Padma, 2020; Salehi, 2021), have shown increasing participation in quantum research, significantly eroding the developed countries' lead (i.e. Germany, Japan, England, Italy) in the global quantum technology race.
Funding information
This work is supported by National Key R&D Program of China (Grant No. 2019YFA0707201), and the open fund of ISTIC-Springer Nature Joint Lab for Open Science (Grant No. HX20211292).
Author contributions
Yuqi Wang (wangyuqi2019@126.com): Conceptualization (Equal), Data curation (Equal), Methodology (Equal); Yue Chen (chenyuedlut@163.com): Conceptualization (Equal), Methodology (Equal); Zhiqi Wang (zhiqi_wang@dlut.edu.cn): Formal analysis (Supporting); Kang Wang (wangkangdult@163.com): Data curation (Equal); Kai Song (Songkai1105@mail.dlut.edu.cn): Formal analysis (Supporting).