Extracting a function encoded in amplitudes of a quantum state by tensor network and orthogonal function expansion

• Item type: SIG Technical Reports(1)
• 公開日: 2022-10-20
• タイトル: Extracting a function encoded in amplitudes of a quantum state by tensor network and orthogonal function expansion
• タイトル / 言語: en
• タイトル: Extracting a function encoded in amplitudes of a quantum state by tensor network and orthogonal function expansion
• 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: Center for Quantum Information and Quantum Biology, Osaka University／JST, PRESTO／Computational Materials Science Research Team, RIKEN Center for Computational Science (R-CCS)
• 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): Center for Quantum Information and Quantum Biology, Osaka University / JST, PRESTO / Computational Materials Science Research Team, RIKEN Center for Computational Science (R-CCS)
• 著者名: Koichi, Miyamoto; Hiroshi, Ueda
• 著者名(英): Koichi, Miyamoto; Hiroshi, Ueda
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: There are some quantum algorithms on problems to find the functions satisfying the given conditions, such as solving partial differential equations, and they claim the exponential quantum speedup compared to the classical methods. However, they in general output the quantum state in which the solution function is encoded in the amplitudes, and reading out the function values as classical data from such a state can be so time-consuming that the quantum speedup is ruined. In this paper, we propose a general method to such a function readout task. We approximate the function by orthogonal function expansion. Besides, in order to avoid the exponential increase of the parameter number for the high-dimensional function, we use the tensor network that approximately reproduces the expansion coefficients as a high-order tensor. We present the quantum circuit that encodes such a tensor network-based function approximation and the procedure to optimize the circuit and obtain the approximating function. We also conduct the numerical experiment to approximate some finance-motivated function and observe that our method works.
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: There are some quantum algorithms on problems to find the functions satisfying the given conditions, such as solving partial differential equations, and they claim the exponential quantum speedup compared to the classical methods. However, they in general output the quantum state in which the solution function is encoded in the amplitudes, and reading out the function values as classical data from such a state can be so time-consuming that the quantum speedup is ruined. In this paper, we propose a general method to such a function readout task. We approximate the function by orthogonal function expansion. Besides, in order to avoid the exponential increase of the parameter number for the high-dimensional function, we use the tensor network that approximately reproduces the expansion coefficients as a high-order tensor. We present the quantum circuit that encodes such a tensor network-based function approximation and the procedure to optimize the circuit and obtain the approximating function. We also conduct the numerical experiment to approximate some finance-motivated function and observe that our method works.
• 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 4, p. 1-10, 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