A hybrid framework for estimating nonlinear functions of quantum states

Estimating nonlinear functions of quantum states, such as the moment \tr(\rho^m), is of fundamental and practical interest in quantum science and technology. Here we show a quantum-classical hybrid framework to measure them, where the quantum part is constituted by the generalized swap test, and the classical part is realized by postprocessing the result from randomized measurements. This hybrid framework utilizes the partial coherent power of the intermediate-scale quantum processor and, at the same time, dramatically reduces the number of quantum measurements and the cost of classical postprocessing. We demonstrate the advantage of our framework in the tasks of state-moment estimation and quantum error mitigation.Comment: v1:5+17 pages, 9 figures; v2:enhance the presentation, clarify the advantages, especially updates Figure 3 and add Table

A hybrid framework for estimating nonlinear functions of quantum states

Abstract Estimating nonlinear functions of quantum states, such as the moment $${{{\rm{tr}}}}({\rho }^{m})$$ tr ( ρ m ) , is of fundamental and practical interest in quantum science and technology. Here we show a quantum-classical hybrid framework to measure them, where the quantum part is constituted by the generalized swap test, and the classical part is realized by postprocessing the result from randomized measurements. This hybrid framework utilizes the partial coherent power of the intermediate-scale quantum processor and, at the same time, dramatically reduces the number of quantum measurements and the cost of classical postprocessing. We demonstrate the advantage of our framework in the tasks of state-moment estimation and quantum error mitigation

The Warming Effect of Urbanization in the Urban Agglomeration Area Accelerates Vegetation Growth on the Urban–Rural Gradient

Urbanization has changed the environmental conditions of vegetation growth, such as the heat island effect, which has an indirect impact on vegetation growth. However, the extent to which the direct and indirect effects of the thermal environment changes caused by urbanization on vegetation growth are unclear. In this study, taking the example of the Guangdong–Hong Kong–Macao Greater Bay Area, a fast-growing national urban agglomeration in China, the relationship between vegetation growth and warming conditions during the period from 2001 to 2020 were explored by the net primary productivity (NPP) and land surface temperature (LST), based on the vegetation growth theory, in urban environments. The results show that there is a significant exponential relationship between the warming and the growth of large-scale vegetation. This relationship is mainly attributable to thermal environmental factors, since their multi-year average contribution rate on the interannual scale is 95.02%. The contribution rate varies on the seasonal scale, according to which the contribution rate is the largest in autumn and the smallest in winter. This research is of great significance for predicting the potential response of vegetation growth to future climate warming and improving vegetation growth in urban areas

The Warming Effect of Urbanization in the Urban Agglomeration Area Accelerates Vegetation Growth on the Urban–Rural Gradient

Urbanization has changed the environmental conditions of vegetation growth, such as the heat island effect, which has an indirect impact on vegetation growth. However, the extent to which the direct and indirect effects of the thermal environment changes caused by urbanization on vegetation growth are unclear. In this study, taking the example of the Guangdong–Hong Kong–Macao Greater Bay Area, a fast-growing national urban agglomeration in China, the relationship between vegetation growth and warming conditions during the period from 2001 to 2020 were explored by the net primary productivity (NPP) and land surface temperature (LST), based on the vegetation growth theory, in urban environments. The results show that there is a significant exponential relationship between the warming and the growth of large-scale vegetation. This relationship is mainly attributable to thermal environmental factors, since their multi-year average contribution rate on the interannual scale is 95.02%. The contribution rate varies on the seasonal scale, according to which the contribution rate is the largest in autumn and the smallest in winter. This research is of great significance for predicting the potential response of vegetation growth to future climate warming and improving vegetation growth in urban areas

Distinguishing the Impacts of Rapid Urbanization on Ecosystem Service Trade-Offs and Synergies: A Case Study of Shenzhen, China

Cities and urban areas are an important part of global sustainable development, and the health and well-being of urban residents are closely related to the quality, quantity, and diversity of urban ecosystem services. Although the rapid urbanization process has changed the structure and function of urban ecosystems, which is notably different from natural ecosystems, the affected ecosystem services and their interactions—the trade-off impact of urbanization intensity on ecosystem services—remain to be discussed. Using land use/land cover and impervious surface area remote sensing datasets, and InVEST and RUSLE-related ecosystem services models to evaluate seven typical ecosystem services in Shenzhen, this study explored the evolution of multiple ecosystem service trade-offs and synergies during the transition from a natural ecosystem to an urban ecosystem, and how they are affected by urbanization intensity through correlation analysis and a discrete time-step simulation model. The results show that: (1) from 1978 to 2018, in the process of ecosystem transformation, grain production dropped from 228,795 tons to 11,733 tons, fruit production peaked in 1990 at 271,508 tons, and service capacity of both showed obvious degradation. Conversely, the cultural service capacity was remarkably enhanced. (2) With the increase in urbanization level, the trade-off and synergy of ecosystem services gradually transition from linear to nonlinear. The rapid urbanization process drives the nonlinear degradation of ecosystem services and the nonlinear enhancement of synergy. (3) Over the past four decades, ecosystem service bundles within the same kilometer grid have shown a quadratic curve-like decrease with increasing impervious surface area, slowly in the early stages and faster in the later stages. This study concludes that urbanization intensity has a significant impact on ecosystem service trade-offs, which can provide support for the formulation of ecological protection and restoration strategies in territorial space based on ecosystem services

Distinguishing the Impacts of Rapid Urbanization on Ecosystem Service Trade-Offs and Synergies: A Case Study of Shenzhen, China

Cities and urban areas are an important part of global sustainable development, and the health and well-being of urban residents are closely related to the quality, quantity, and diversity of urban ecosystem services. Although the rapid urbanization process has changed the structure and function of urban ecosystems, which is notably different from natural ecosystems, the affected ecosystem services and their interactions—the trade-off impact of urbanization intensity on ecosystem services—remain to be discussed. Using land use/land cover and impervious surface area remote sensing datasets, and InVEST and RUSLE-related ecosystem services models to evaluate seven typical ecosystem services in Shenzhen, this study explored the evolution of multiple ecosystem service trade-offs and synergies during the transition from a natural ecosystem to an urban ecosystem, and how they are affected by urbanization intensity through correlation analysis and a discrete time-step simulation model. The results show that: (1) from 1978 to 2018, in the process of ecosystem transformation, grain production dropped from 228,795 tons to 11,733 tons, fruit production peaked in 1990 at 271,508 tons, and service capacity of both showed obvious degradation. Conversely, the cultural service capacity was remarkably enhanced. (2) With the increase in urbanization level, the trade-off and synergy of ecosystem services gradually transition from linear to nonlinear. The rapid urbanization process drives the nonlinear degradation of ecosystem services and the nonlinear enhancement of synergy. (3) Over the past four decades, ecosystem service bundles within the same kilometer grid have shown a quadratic curve-like decrease with increasing impervious surface area, slowly in the early stages and faster in the later stages. This study concludes that urbanization intensity has a significant impact on ecosystem service trade-offs, which can provide support for the formulation of ecological protection and restoration strategies in territorial space based on ecosystem services