A Novel Metric for Assessing National Strength in Scientific Research: Understanding China's Research Output in Quantum Technology through Collaboration

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 (SS_i): a. the national contribution to academic impact (CT_i), b. the national scientific self-reliance for a country (SR_i). The metric model of national strength in scientific research is designed as follows: (1) SSi=CTi*SRi S{S_i} = C{T_i}*S{R_i} Where SS_i is the scientific research strength index of country i, CT_i is the academic contribution of country i, SR_i is the national scientific self-reliance index of country i.

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: (2) CTi=∑m∈mi[ VM+VM*d*(α∑n=1M−m1M−n−β) ] C{T_i} = \sum\limits_{m \in {m_i}} {\left[ {{V \over M} + {V \over M}*d*\left( {\alpha \sum\limits_{n = 1}^{M - m} {{1 \over {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), m_i is a set of the order of authorship belonging to country i. d is the author contribution transfer factor (d = 0.5). α is the contribution benefit coefficient (α = 1), β is the contribution loss coefficient (β = 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 β = 0. If the author is in the last position, there will be no contribution gain for the author, then α = 0.

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. (3) SRi=NitSit∑j∈Corpi(NijtNit*Autonomyi→j)+(1−NitSit)*Autonomyindep S{R_i} = {{N_i^t} \over {S_i^t}}\sum\limits_{j \in Cor{p_i}} {\left( {{{N_{ij}^t} \over {N_i^t}}*Autonom{y_{i \to j}}} \right) + \left( {1 - {{N_i^t} \over {S_i^t}}} \right)*Autonom{y_{indep}}} where Nit N_i^t is the total number of cooperative papers produced by country i with other countries at time t, Sit S_i^t is the total number of papers produced by country i at time t. Corp_i is the set of cooperating countries for country i. Nijt 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 (1−NitSit) \left( {1 - {{N_i^t} \over {S_i^t}}} \right) is the proportion of independently published papers in the country i, Autonomy_indep 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 NitSit {{N_i^t} \over {S_i^t}} is the proportion of multi-countries papers published by country i, Autonomy_i→j is the research autonomy index of country i in research collaboration between countries i and j. ∑j∈Corpi(NijtNit*Autonomyi→j) \sum\limits_{j \in Cor{p_i}} {\left( {{{N_{ij}^t} \over {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 (Autonomy_i→j) is calculated by subtracting the dominant degree of country j (Dominantj→it) \left( {{Dominant}_{j \to i}^t} \right) from the dominant degree of country i (Dominanti→jt) \left( {{Dominant}_{i \to j}^t} \right) . The calculation method is as follows: (4) Autonomyi→j=Dominanti→jt−Dominantj→it {\rm{Autonom}}{{\rm{y}}_{i \to j}} = {Dominant}_{i \to j}^t - {Dominant}_{j \to i}^t Where the research autonomy index (Autonomy_i→j) takes values in the range (−1,1), if Autonomy_i→j ≤ 0, then country i has no research autonomy with country j. if Autonomy_i→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 (CT_i) 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 (Dominanti→jt) \left( {{Dominant}_{i \to j}^t} \right) . The sum of the five weights w_k is 1, and their values are equidistantly decreasing in order, that is, 5/15, 4/15, 3/15, 2/15, 1/15 respectively. (5) Dominanti→jt=∑k−15Nki→jt WkNijt {Dominant}_{i \to j}^t = {{\sum\nolimits_{k - 1}^5 {N_{{k_{i \to j}}}^t\,{W_k}} } \over {N_{ij}^t}} Where Nki→jt 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 (w_k). Nijt N_{ij}^t is the total number of collaborative papers of country i and country j at time t. The greater Dominanti→jt {Dominant}_{i \to j}^t indicates, the stronger the leading role played by country i to country j at time t.

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.

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).

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

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

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 6^th, degree ranked 5^th, and Closeness ranked 5^th, well below the 2^nd ranking by papers amount (see Table 4).

Based on the proposed indicator CT_i (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)

Figure 3

CT see Equation 2 in Section 2. Contribution Proportioni=CTiTotal CT \text{Contribution}\ \text{Proportio}{{\text{n}}_{i}}={}^{C{{T}_{i}}}\!\!\diagup\!\!{}_{Total\ CT}\

In this section, we try to understand China's research autonomy in quantum scientific collaboration through the research autonomy index (Autonomy_i→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 (Autonomy_China→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.

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 9^th 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.

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.

The national scientific self-reliance index (SR_i) 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

Fig. 5 shows that the US's SS ranked first between 2001 and 2011, but China overpassed the US and became the top one based on SS. The SS rankings of Japan, Germany, Italy, and England have fallen in the past 10 years but are still among the top 10 SS rankings in the world. China is the unique developing country in the top 5 SS rankings and has been ranked 1st since 2012, surpassing the US to become the global leader in the quantum technology area.

Figure 5

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.