Quantum Speedup of Monte Carlo Integration with respect to the Number of Dimensions and its Application to Finance

• Item type: SIG Technical Reports(1)
• 公開日: 2021-03-22
• タイトル: Quantum Speedup of Monte Carlo Integration with respect to the Number of Dimensions and its Application to Finance
• タイトル / 言語: en
• タイトル: Quantum Speedup of Monte Carlo Integration with respect to the Number of Dimensions and its Application to Finance
• 言語: eng
• 資源タイプ / 資源タイプ識別子: http://purl.org/coar/resource_type/c_18gh
• 資源タイプ: technical report
• 著者所属: Mizuho-DL Financial Technology Co., Ltd.
• 著者所属: Center for Quantum Information and Quantum Biology, Institute for Open and Transdisciplinary Research Initiatives, Osaka University／Mizuho-DL Financial Technology Co., Ltd.
• 著者所属: Mizuho-DL Financial Technology Co., Ltd.
• 著者所属: Mizuho-DL Financial Technology Co., Ltd.
• 著者所属(英): en
• 著者所属(英): Mizuho-DL Financial Technology Co., Ltd.
• 著者所属(英): en
• 著者所属(英): Center for Quantum Information and Quantum Biology, Institute for Open and Transdisciplinary Research Initiatives, Osaka University / Mizuho-DL Financial Technology Co., Ltd.
• 著者所属(英): en
• 著者所属(英): Mizuho-DL Financial Technology Co., Ltd.
• 著者所属(英): en
• 著者所属(英): Mizuho-DL Financial Technology Co., Ltd.
• 著者名: Kazuya, Kaneko; Koichi, Miyamoto; Naoyuki, Takeda; Kazuyoshi, Yoshino
• 著者名(英): Kazuya, Kaneko; Koichi, Miyamoto; Naoyuki, Takeda; Kazuyoshi, Yoshino
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: Monte Carlo integration (MC) using quantum computers has been widely investigated, including applications to concrete problems. It is known that quantum algorithms based on quantum amplitude estimation (QAE) can compute an integral with a smaller number of iterative calls of the quantum circuit which calculates the integrand, than classical methods call the integrand subroutine. However, the issues about the iterative operations in the integrand circuit have not been discussed so much. That is, in the high-dimensional integration, many random numbers are used for calculation of the integrand and in some cases similar calculations are repeated to obtain one sample value of the integrand. In this paper, we point out that we can reduce the number of such repeated operations by a combination of the nested QAE and the use of pseudorandom numbers (PRNs), if the integrand has the separable form with respect to contributions from distinct random numbers. The use of PRNs, which the authors originally proposed in the context of the quantum algorithm for MC, is the key factor also in this paper, since it enables parallel computation of the separable terms in the integrand. Furthermore, we pick up one use case of this method in finance, the credit portfolio risk measurement, and estimate to what extent the complexity is reduced.
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: Monte Carlo integration (MC) using quantum computers has been widely investigated, including applications to concrete problems. It is known that quantum algorithms based on quantum amplitude estimation (QAE) can compute an integral with a smaller number of iterative calls of the quantum circuit which calculates the integrand, than classical methods call the integrand subroutine. However, the issues about the iterative operations in the integrand circuit have not been discussed so much. That is, in the high-dimensional integration, many random numbers are used for calculation of the integrand and in some cases similar calculations are repeated to obtain one sample value of the integrand. In this paper, we point out that we can reduce the number of such repeated operations by a combination of the nested QAE and the use of pseudorandom numbers (PRNs), if the integrand has the separable form with respect to contributions from distinct random numbers. The use of PRNs, which the authors originally proposed in the context of the quantum algorithm for MC, is the key factor also in this paper, since it enables parallel computation of the separable terms in the integrand. Furthermore, we pick up one use case of this method in finance, the credit portfolio risk measurement, and estimate to what extent the complexity is reduced.
• 書誌レコードID / 収録物識別子タイプ: NCID
• 書誌レコードID / 収録物識別子: AA12894105
• 書誌情報: 研究報告量子ソフトウェア（QS）; 巻 2021-QS-2, 号 15, p. 1-10, 発行日 2021-03-22
• ISSN / 収録物識別子タイプ: ISSN
• ISSN / 収録物識別子: 2435-6492
• Notice: SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc.
• 出版者 / 言語: ja
• 出版者: 情報処理学会