Abstract
Quantum computing has been much attention as one of the new computational principles. In particular, annealing machines that use the Ising model of statistical mechanics are emerging and feasible next-generation computational technology. Annealing machines can solve combinatorial optimization problems that have been considered difficult to solve in classical computing principles. Currently, Ising-based algorithms are being vigorously developed to perform various applications such as machine learning by solving them as combinatorial optimization problems. On the other hand, the amount of data, such as sensor data and simulation data, used in machine learning applications is drastically increasing. It becomes difficult to handle large amounts of data. In particular, since the number of qubits of annealing machines is limited, Ising-based algorithms independent of data size are strongly required.
This paper focuses on Ising-based linear regression that utilizes a precision vector instead of each data element of target data. Although the use of a precision vector is a key point that can reduce the number of qubits against the amount of data, detail such as how many elements of a precision vector is necessary and how these elements are set to be is not clarified yet. This paper discusses the characteristics of a precision vector through performance evaluation of Ising-based linear regression with a practical data set in empirical ways.
The experimental results show that a proper precision vector considering the input data set can improve the quality of the linear regression.
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Acknowledgments
This research was partially supported by MEXT Next Generation High-Performance Computing Infrastructures and Applications R &D Program, entitled “R &D of A Quantum-Annealing-Assisted Next Generation HPC Infrastructure and its Applications,” Japan-Russia Research Cooperative Program between JSPS and RFBR, Grant number JPJSBP120214801, Grants-in-Aid for Scientific Research (A) #19H01095, and Grants-in-Aid for Scientific Research (C) #20K11838.
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Aoyama, K., Komatsu, K., Kumagai, M., Kobayashi, H. (2023). Analysis of Precision Vectors for Ising-Based Linear Regression. In: Takizawa, H., Shen, H., Hanawa, T., Hyuk Park, J., Tian, H., Egawa, R. (eds) Parallel and Distributed Computing, Applications and Technologies. PDCAT 2022. Lecture Notes in Computer Science, vol 13798. Springer, Cham. https://doi.org/10.1007/978-3-031-29927-8_20
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DOI: https://doi.org/10.1007/978-3-031-29927-8_20
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