The solution accuracy of the Original Quantum machine learning algorithm has been exponentially improved

Recently, the cooperation between Origin Quantum and the HASM research team of the State Key Laboratory of Resource and Environmental Information Systems of the Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences has made important progress. Based on the open source quantum programming framework QPanda of Yuanyuan Quantum, to realize the programming of related quantum algorithms, and using the HASM-HHL quantum machine learning algorithm, the researchers realized the digital terrain model (DTM) downscaling of Wugong Mountain in Jiangxi Province, and studied a variety of calculations Under the accuracy, the change process of the quantum circuit corresponding to the algorithm verifies that under ideal conditions, the HHL quantum algorithm simulated by the supercomputing program can not only achieve the calculation accuracy of the classical preprocessing conjugate gradient method, but also the algorithm complexity is compared with that of the classical algorithm. effectively reduced. The research results were recently published in Science Bulletin.

How to use a theoretically complete method to realize the effective integration of extrinsic information (such as satellite remote sensing information) and intrinsic information (such as ground observation information), and to solve the error problem, multi-scale problem and nonlinear problem of ecological environment surface modeling And the problem of large memory requirements has always been an important challenge faced by eco-environmental informatics. In order to solve the above problems, the researchers abstracted the grid expression of ecological environment elements into a mathematical "surface", and through the organic combination of surface theory, system theory and optimization control theory and modern computer technology, created an integrated external and internal accumulation. A high-accuracy surface modeling (HASM) method for aggregate information. However, HASM still has many remaining problems to be solved.

Quantum circuits in HASM-HHL

The high-precision surface modeling (HASM) method can convert the surface modeling of spatial ecological environment elements into solving large-scale sparse linear algebraic equations, which can be solved using the HHL quantum algorithm. The researchers refer to the coupling of HASM machine learning with the HHL quantum algorithm as HASM-HHL quantum machine learning.

In this study, based on theoretical research and numerical experiments on the global prediction capability of HASM, the research team selected Wugong Mountain in Jiangxi Province as the case area to carry out empirical research, and conducted quantum algorithm simulations through the distributed computing framework provided by QPanda. Training experiments show that the precision setting has a large impact on the HASM-HHL performance and quantum circuit parameters; the total number of qubits required for quantum computing depends on the total number of grids in the computational domain. It is estimated that when HASM-HHL is used to simulate the entire Earth's surface, 40 qubits are required at a spatial resolution of 1 km × 1 km, and 45 qubits are required at a spatial resolution of 1 m × 1 m. The results show that under the condition of sufficient physical quantum computing resources, the HASM-HHL algorithm has higher solution accuracy, and has an exponential acceleration effect compared to the classical algorithm.

Relationship between computational domain size and total number of qubits required to operate HASM-HHL

Since HASM has been successfully applied to the construction of digital elevation models at various spatial scales, as well as the simulation analysis of changes in ecological diversity, population dynamics, soil property dynamics, food supply dynamics, carbon storage dynamics, carbon dioxide concentration changes, climate change, and the dynamics of the spread of COVID-19, etc. . The birth of the HASM-HHL algorithm provides a new algorithm framework for the aforementioned various numerical applications, and also provides new ideas for more complex computing problems in the future. In the future, HASM-HHL is expected to be more widely used in the field of simulating and analyzing the earth's surface system and its ecological environment elements.

Note: The research results were supported by the National Natural Science Foundation of China Key Project (Grant No. 41930647).

References:

[1] TianXiang Yue, Yi Liu, ZhengPing Du, John Wilson, DongYi Zhao, Yu Wang, Na Zhao, WenJiao Shi, ZeMeng Fan, XiaoMin Zhao, Qing Zhang, HongSheng Huang, QingYuan Wu, Wei Zhou, YiMen Jiao, Zhe Xu , SaiBo Li, Yang Yang, BoJie Fu. 2022. Quantum machine learning of eco-environmental surfaces. Science Bulletin https.

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[3] QPanda2: https://github.com/OriginQ/QPanda-2

[4] Weicheng Kong, Junchao Wang, Yongjian Han, Yuchun Wu, Origin Pilot: a Quantum Operating System for Effecient Usage of Quantum Resources. arXiv:2105.10730v1

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