Dividing quantum circuits for time evolution of stochastic processes by orthogonal series density estimation

• Item type: SIG Technical Reports(1)
• 公開日: 2024-10-21
• タイトル: Dividing quantum circuits for time evolution of stochastic processes by orthogonal series density estimation
• タイトル / 言語: en
• タイトル: Dividing quantum circuits for time evolution of stochastic processes by orthogonal series density estimation
• 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(英): en
• 著者所属(英): Center for Quantum Information and Quantum Biology, Osaka University
• 著者名: Koichi, Miyamoto
• 著者名(英): Koichi, Miyamoto
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: Quantum Monte Carlo integration (QMCI) is a quantum algorithm to estimate expectations of random variables, with industrial applications such as financial derivative pricing. When it is applied to expectations concerning a stochastic process X(t), e.g., an underlying asset price in derivative pricing, the quantum circuit UX(t) to generate the quantum state encoding the probability density of X(t) can have a large depth. With time discretized into N points, using state preparation oracles for the transition probabilities of X(t), the state preparation for X(t) results in a depth of O(N), which may be problematic for large N. Moreover, if we estimate expectations concerning X(t) at N time points, the total query complexity scales on N as O(N2), which is worse than the O(N) complexity in the classical Monte Carlo method. In this paper, to improve this, we propose a method to divide UX(t) based on orthogonal series density estimation. This approach involves approximating the densities of X(t) at N time points with orthogonal series, where the coefficients are estimated as expectations of the orthogonal functions by QMCI. By using these approximated densities, we can estimate expectations concerning X(t) by QMCI without requiring deep circuits. To obtain the densities at N time points, our method achieves the circuit depth and total query complexity scaling as O(√N) and O(N3/2), respectively. (This is the 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: Quantum Monte Carlo integration (QMCI) is a quantum algorithm to estimate expectations of random variables, with industrial applications such as financial derivative pricing. When it is applied to expectations concerning a stochastic process X(t), e.g., an underlying asset price in derivative pricing, the quantum circuit UX(t) to generate the quantum state encoding the probability density of X(t) can have a large depth. With time discretized into N points, using state preparation oracles for the transition probabilities of X(t), the state preparation for X(t) results in a depth of O(N), which may be problematic for large N. Moreover, if we estimate expectations concerning X(t) at N time points, the total query complexity scales on N as O(N2), which is worse than the O(N) complexity in the classical Monte Carlo method. In this paper, to improve this, we propose a method to divide UX(t) based on orthogonal series density estimation. This approach involves approximating the densities of X(t) at N time points with orthogonal series, where the coefficients are estimated as expectations of the orthogonal functions by QMCI. By using these approximated densities, we can estimate expectations concerning X(t) by QMCI without requiring deep circuits. To obtain the densities at N time points, our method achieves the circuit depth and total query complexity scaling as O(√N) and O(N3/2), respectively. (This is the 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-13, 号 10, p. 1-10, 発行日 2024-10-21
• 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