Quantum algorithm for the Vlasov simulation of the large-scale structure formation with massive neutrinos

• Item type: SIG Technical Reports(1)
• 公開日: 2024-03-21
• タイトル: Quantum algorithm for the Vlasov simulation of the large-scale structure formation with massive neutrinos
• タイトル / 言語: en
• タイトル: Quantum algorithm for the Vlasov simulation of the large-scale structure formation with massive neutrinos
• 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: Center for Quantum Information and Quantum Biology, Osaka University
• 著者所属: Department of Physics, Graduate School of Science, The University of Tokyo
• 著者所属: Department of Physics, Graduate School of Science, The University of Tokyo／Research Center for the Early Universe, Graduate School of Science, The University of Tokyo
• 著者所属: Department of Liberal Arts, Tokyo University of Technology／Research Center for the Early Universe, Graduate School of Science, The University of Tokyo
• 著者所属: Department of Physics, Graduate School of Science, The University of Tokyo／Kavli IPMU (WPI), The University of Tokyo Institutes for Advanced Study (UTIAS), The University of Tokyo
• 著者所属(英): en
• 著者所属(英): Center for Quantum Information and Quantum Biology, Osaka University
• 著者所属(英): en
• 著者所属(英): Department of Physics, Graduate School of Science, The University of Tokyo
• 著者所属(英): en
• 著者所属(英): Department of Physics, Graduate School of Science, The University of Tokyo / Research Center for the Early Universe, Graduate School of Science, The University of Tokyo
• 著者所属(英): en
• 著者所属(英): Department of Liberal Arts, Tokyo University of Technology / Research Center for the Early Universe, Graduate School of Science, The University of Tokyo
• 著者所属(英): en
• 著者所属(英): Department of Physics, Graduate School of Science, The University of Tokyo / Kavli IPMU (WPI), The University of Tokyo Institutes for Advanced Study (UTIAS), The University of Tokyo
• 著者名: Koichi, Miyamoto; Soichiro, Yamazaki; Fumio, Uchida; Kotaro, Fujisawa; Naoki, Yoshida
• 著者名(英): Koichi, Miyamoto; Soichiro, Yamazaki; Fumio, Uchida; Kotaro, Fujisawa; Naoki, Yoshida
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: Investigating the cosmological implication of the fact that neutrino has finite mass is of importance for fundamental physics. In particular, massive neutrino affects the formation of the large-scale structure (LSS) of the universe, and conversely, observations of the LSS can give constraints on the neutrino mass. Numerical simulations of the LSS formation including massive neutrino along with conventional cold dark matter is thus an important task. For this, calculating the neutrino distribution in the phase space by solving the Vlasov equation is a suitable approach, but it requires solving the PDE in the (6+1)-dimensional space and is thus computationally demanding: configuring ngr grid points in each coordinate and nt time grid points leads to O(n6gr) memory space and O(ntn6gr) queries to the coefficients in the discretized PDE. We propose a quantum algorithm for this task. Linearizing the Vlasov equation by neglecting the relatively weak self-gravity of the neutrino, we perform the Hamiltonian simulation to produce quantum states that encode the phase space distribution of neutrino. We also propose a way to extract the power spectrum of the neutrino density perturbations as classical data from the quantum state by quantum amplitude estimation with accuracy ε and query complexity of order O((ngr +nt)/ε). Our method also reduces the space complexity to O(polylog(ngr/ε)) in terms of the qubit number, while using quantum random access memories with O(n3gr) entries. As far as we know, this is the first quantum algorithm for the LSS simulation that outputs the quantity of practical interest with guaranteed accuracy. (This is a short version of the full paper [1].)
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: Investigating the cosmological implication of the fact that neutrino has finite mass is of importance for fundamental physics. In particular, massive neutrino affects the formation of the large-scale structure (LSS) of the universe, and conversely, observations of the LSS can give constraints on the neutrino mass. Numerical simulations of the LSS formation including massive neutrino along with conventional cold dark matter is thus an important task. For this, calculating the neutrino distribution in the phase space by solving the Vlasov equation is a suitable approach, but it requires solving the PDE in the (6+1)-dimensional space and is thus computationally demanding: configuring ngr grid points in each coordinate and nt time grid points leads to O(n6gr) memory space and O(ntn6gr) queries to the coefficients in the discretized PDE. We propose a quantum algorithm for this task. Linearizing the Vlasov equation by neglecting the relatively weak self-gravity of the neutrino, we perform the Hamiltonian simulation to produce quantum states that encode the phase space distribution of neutrino. We also propose a way to extract the power spectrum of the neutrino density perturbations as classical data from the quantum state by quantum amplitude estimation with accuracy ε and query complexity of order O((ngr +nt)/ε). Our method also reduces the space complexity to O(polylog(ngr/ε)) in terms of the qubit number, while using quantum random access memories with O(n3gr) entries. As far as we know, this is the first quantum algorithm for the LSS simulation that outputs the quantity of practical interest with guaranteed accuracy. (This is a short version of the full paper [1].)
• 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 2024-QS-11, 号 1, p. 1-10, 発行日 2024-03-21
• 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