Hamiltonian simulation using quantum singular value transformation: a detailed complexity analysis and application to simulating the linearized Vlasov-Poisson equation

• Item type: SIG Technical Reports(1)
• 公開日: 2022-10-20
• タイトル: Hamiltonian simulation using quantum singular value transformation: a detailed complexity analysis and application to simulating the linearized Vlasov-Poisson equation
• タイトル / 言語: en
• タイトル: Hamiltonian simulation using quantum singular value transformation: a detailed complexity analysis and application to simulating the linearized Vlasov-Poisson equation
• 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: Graduate School of Science and Technology, Keio University
• 著者所属: Graduate School of Science and Technology, Keio University
• 著者所属: Graduate School of Science and Technology, Keio University
• 著者所属(英): en
• 著者所属(英): Graduate School of Science and Technology, Keio University
• 著者所属(英): en
• 著者所属(英): Graduate School of Science and Technology, Keio University
• 著者所属(英): en
• 著者所属(英): Graduate School of Science and Technology, Keio University
• 著者名: Kiichiro, Toyoizumi; Naoki, Yamamoto; Kazuo, Hoshino
• 著者名(英): Kiichiro, Toyoizumi; Naoki, Yamamoto; Kazuo, Hoshino
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: Quantum computing can be used to speed up the simulation time (more precisely, the number of queries of the algorithm) for physical systems; one such promising approach is the Hamiltonian simulation (HS) algorithm. Recently, it was proven that the quantum singular value transformation (QSVT) achieves the minimum simulation time for HS. An important subroutine of the QSVT-based HS algorithm is the amplitude amplification operation, which can be realized via the oblivious amplitude amplification or the fixed-point amplitude amplification in the QSVT framework. In this work, we execute a detailed analysis of the error and simulation time of the QSVT-based HS and show that the oblivious method is better than the fixed-point one in the sense of simulation time for a given error tolerance. Based on this finding, we apply the QSVT-based HS to the one-dimensional linearized Vlasov-Poisson equation and demonstrate that the linear Landau damping can be successfully simulated.
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: Quantum computing can be used to speed up the simulation time (more precisely, the number of queries of the algorithm) for physical systems; one such promising approach is the Hamiltonian simulation (HS) algorithm. Recently, it was proven that the quantum singular value transformation (QSVT) achieves the minimum simulation time for HS. An important subroutine of the QSVT-based HS algorithm is the amplitude amplification operation, which can be realized via the oblivious amplitude amplification or the fixed-point amplitude amplification in the QSVT framework. In this work, we execute a detailed analysis of the error and simulation time of the QSVT-based HS and show that the oblivious method is better than the fixed-point one in the sense of simulation time for a given error tolerance. Based on this finding, we apply the QSVT-based HS to the one-dimensional linearized Vlasov-Poisson equation and demonstrate that the linear Landau damping can be successfully simulated.
• 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 2022-QS-7, 号 2, p. 1-7, 発行日 2022-10-20
• 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