蒙特卡罗期权定价的量子优势

IF 1.1 Q3 PHYSICS, MULTIDISCIPLINARY
Zoltán Udvarnoki, G. Fáth, N. Fogarasi
{"title":"蒙特卡罗期权定价的量子优势","authors":"Zoltán Udvarnoki, G. Fáth, N. Fogarasi","doi":"10.1088/2399-6528/acd2a4","DOIUrl":null,"url":null,"abstract":"Quantum computers have the potential to provide quadratic speedup for Monte Carlo methods currently used in various classical applications. In this work, we examine the advantage of quantum computers for financial option pricing with the Monte Carlo method. Systematic and statistical errors are handled in a joint framework, and a relationship to quantum gate error is established. New metrics are introduced for the assessment of quantum advantage based on sample count and optimized error handling. We implement and analyze a Fourier series based approach and demonstrate its benefit over the more traditional rescaling method in function approximation. Our numerical calculations reveal the unpredictable nature of systematic errors, making consistent quantum advantage difficult with current quantum hardware. Our results indicate that very low noise levels, a two-qubit gate error rate below 10−6, are necessary for the quantum method to outperform the classical one, but a low number of logical qubits (ca. 20) may be sufficient to see quantum advantage already.","PeriodicalId":47089,"journal":{"name":"Journal of Physics Communications","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quantum advantage of Monte Carlo option pricing\",\"authors\":\"Zoltán Udvarnoki, G. Fáth, N. Fogarasi\",\"doi\":\"10.1088/2399-6528/acd2a4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Quantum computers have the potential to provide quadratic speedup for Monte Carlo methods currently used in various classical applications. In this work, we examine the advantage of quantum computers for financial option pricing with the Monte Carlo method. Systematic and statistical errors are handled in a joint framework, and a relationship to quantum gate error is established. New metrics are introduced for the assessment of quantum advantage based on sample count and optimized error handling. We implement and analyze a Fourier series based approach and demonstrate its benefit over the more traditional rescaling method in function approximation. Our numerical calculations reveal the unpredictable nature of systematic errors, making consistent quantum advantage difficult with current quantum hardware. Our results indicate that very low noise levels, a two-qubit gate error rate below 10−6, are necessary for the quantum method to outperform the classical one, but a low number of logical qubits (ca. 20) may be sufficient to see quantum advantage already.\",\"PeriodicalId\":47089,\"journal\":{\"name\":\"Journal of Physics Communications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2023-05-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Physics Communications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1088/2399-6528/acd2a4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Physics Communications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/2399-6528/acd2a4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0

摘要

量子计算机有潜力为目前在各种经典应用中使用的蒙特卡罗方法提供二次加速。在这项工作中,我们用蒙特卡洛方法研究了量子计算机在金融期权定价中的优势。系统误差和统计误差在一个联合框架中处理,并建立了与量子门误差的关系。引入了基于样本计数和优化错误处理的量子优势评估新指标。我们实现并分析了一种基于傅立叶级数的方法,并证明了它在函数近似中优于传统的重标度方法。我们的数值计算揭示了系统误差的不可预测性,使得当前量子硬件难以保持一致的量子优势。我们的研究结果表明,非常低的噪声水平,两个量子比特的门错误率低于10−6,是量子方法优于经典方法所必需的,但是低数量的逻辑量子比特(约20)可能已经足以看到量子优势。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Quantum advantage of Monte Carlo option pricing
Quantum computers have the potential to provide quadratic speedup for Monte Carlo methods currently used in various classical applications. In this work, we examine the advantage of quantum computers for financial option pricing with the Monte Carlo method. Systematic and statistical errors are handled in a joint framework, and a relationship to quantum gate error is established. New metrics are introduced for the assessment of quantum advantage based on sample count and optimized error handling. We implement and analyze a Fourier series based approach and demonstrate its benefit over the more traditional rescaling method in function approximation. Our numerical calculations reveal the unpredictable nature of systematic errors, making consistent quantum advantage difficult with current quantum hardware. Our results indicate that very low noise levels, a two-qubit gate error rate below 10−6, are necessary for the quantum method to outperform the classical one, but a low number of logical qubits (ca. 20) may be sufficient to see quantum advantage already.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Journal of Physics Communications
Journal of Physics Communications PHYSICS, MULTIDISCIPLINARY-
CiteScore
2.60
自引率
0.00%
发文量
114
审稿时长
10 weeks
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信