Quantum signal processing applied to formulate perturbation theory

• Item type: SIG Technical Reports(1)
• 公開日: 2022-10-20
• タイトル: Quantum signal processing applied to formulate perturbation theory
• タイトル / 言語: en
• タイトル: Quantum signal processing applied to formulate perturbation theory
• 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 Engineering Science, Osaka University／Center for Quantum Information and Quantum Biology, Osaka University
• 著者所属: Center for Quantum Information and Quantum Biology, Osaka University
• 著者所属(英): en
• 著者所属(英): Graduate School of Engineering Science, Osaka University / Center for Quantum Information and Quantum Biology, Osaka University
• 著者所属(英): en
• 著者所属(英): Center for Quantum Information and Quantum Biology, Osaka University
• 著者名: Kosuke, Mitarai; Wataru, Mizukami
• 著者名(英): Kosuke, Mitarai; Wataru, Mizukami
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: We provide a quantum algorithm to obtain perturbative energies on quantum computers. The benefit of using quantum computers is that we can start the perturbation from a Hamiltonian that is classically hard to solve. The proposed algorithm uses quantum signal processing (QSP) to achieve this goal. Along with the perturbation theory, we construct a technique for ground state preparation with detailed computational cost analysis, which can be of independent interest. We also estimate a rough computational cost of the algorithm for simple chemical systems such as water clusters and polyacene molecules. Unfortunately, we find that the proposed algorithm, at least in its current form, does not exhibit practical numbers despite of the efficiency of QSP compared to conventional quantum algorithms. However, perturbation theory itself is an attractive direction to explore because of its physical interpretability, that is, it generally provides us insights about what interaction gives an important contribution to the properties of systems. This is in sharp contrast to the conventional approaches based on the quantum phase estimation algorithm, where we can only obtain values of energy. From this aspect, this work is a first step towards “explainable” quantum simulation on fault-tolerant quantum computers.
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: We provide a quantum algorithm to obtain perturbative energies on quantum computers. The benefit of using quantum computers is that we can start the perturbation from a Hamiltonian that is classically hard to solve. The proposed algorithm uses quantum signal processing (QSP) to achieve this goal. Along with the perturbation theory, we construct a technique for ground state preparation with detailed computational cost analysis, which can be of independent interest. We also estimate a rough computational cost of the algorithm for simple chemical systems such as water clusters and polyacene molecules. Unfortunately, we find that the proposed algorithm, at least in its current form, does not exhibit practical numbers despite of the efficiency of QSP compared to conventional quantum algorithms. However, perturbation theory itself is an attractive direction to explore because of its physical interpretability, that is, it generally provides us insights about what interaction gives an important contribution to the properties of systems. This is in sharp contrast to the conventional approaches based on the quantum phase estimation algorithm, where we can only obtain values of energy. From this aspect, this work is a first step towards “explainable” quantum simulation on fault-tolerant quantum computers.
• 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 3, p. 1-6, 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