使用量子计算机模拟金融期权定价的非赫密特动态
Swagat Kumar1,2, Colin Michael Wilmott3
1Department of Mathematics, Nottingham Trent University, Nottingham, NG11 8NS, UK. swagat.kumar@insait.ai.
Scientific reports
|April 17, 2025
概括
这项研究将量子想象时间进化 (QITE) 算法推广到超出了反赫米蒂安汉密尔顿主义者的范围. 这使得能够用量子计算解决部分微分方程,比如选择定价的Black-Scholes方程.
科学领域:
- 量子计算是一种量子计算.
- 计算物理 计算物理
- 金融数学 金融数学
背景情况:
- 施罗丁格方程控制了量子态演变的过程.
- 赫米蒂安汉密尔顿人确保统一的动态.
- 反赫米蒂安汉密尔顿主义者用于虚构的时间进化,以找到基本状态.
研究的目的:
- 为了概括量子想象时间演化 (QITE) 算法.
- 取消QITE对反赫米蒂安汉密尔顿人的限制.
- 解决部分微分方程 (PDEs) 相当于施罗丁格方程与任意的非赫米特汉密尔顿方程.
主要方法:
- 开发了一个通用的QITE方法.
- 应用该方法来解决PDEs,包括Black-Scholes方程.
- 在量子计算机上模拟非单元进化的规范化动态.
主要成果:
- 成功地扩大了QITE对非赫尔密斯汉密尔顿人的范围.
- 证明了一般化QITE的可行性,用于定价欧洲期权合约.
- 展示了一种量子方法来解决布莱克-斯科尔斯方程.
结论:
- 一般化的QITE为量子计算提供了一个强大的新工具.
- 这种方法为金融领域的现实应用提供了可行的量子方法.
- 量子计算可以被利用来解决复杂的金融模型,如布莱克-斯科尔斯方程.
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