Quantum Encoding and Analysis on Continuous Time Stochastic Process with Financial Applications

Xi-Ning Zhuang; Zhao-Yun Chen; Cheng Xue; Yu-Chun Wu; Guo-Ping Guo

doi:10.22331/q-2023-10-03-1127

Quantum Encoding and Analysis on Continuous Time Stochastic Process with Financial Applications

Xi-Ning Zhuang^1,2, Zhao-Yun Chen³, Cheng Xue³, Yu-Chun Wu^1,4,5,3, and Guo-Ping Guo^1,4,5,3,2

¹CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
²Origin Quantum Computing, Hefei, China
³Institute of Artificial Intelligence, Hefei Comprehensive National Science Center
⁴CAS Center for Excellence and Synergistic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
⁵Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China

Published:	2023-10-03, volume 7, page 1127
Eprint:	arXiv:2208.02364v5
Doi:	https://doi.org/10.22331/q-2023-10-03-1127
Citation:	Quantum 7, 1127 (2023).

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Abstract

Modeling stochastic phenomena in continuous time is an essential yet challenging problem. Analytic solutions are often unavailable, and numerical methods can be prohibitively time-consuming and computationally expensive. To address this issue, we propose an algorithmic framework tailored for quantum continuous time stochastic processes. This framework consists of two key procedures: data preparation and information extraction. The data preparation procedure is specifically designed to encode and compress information, resulting in a significant reduction in both space and time complexities. This reduction is exponential with respect to a crucial feature parameter of the stochastic process. Additionally, it can serve as a submodule for other quantum algorithms, mitigating the common data input bottleneck. The information extraction procedure is designed to decode and process compressed information with quadratic acceleration, extending the quantum-enhanced Monte Carlo method. The framework demonstrates versatility and flexibility, finding applications in statistics, physics, time series analysis and finance. Illustrative examples include option pricing in the Merton Jump Diffusion Model and ruin probability computing in the Collective Risk Model, showcasing the framework’s ability to capture extreme market events and incorporate history-dependent information. Overall, this quantum algorithmic framework provides a powerful tool for accurate analysis and enhanced understanding of stochastic phenomena.

Featured image: Featured image: The basic idea of how to encoding the continuous time stochastic process is illustrated. Left: The continuous process is embedded into a discrete sequence of states and their holding time. Middle: For a wide range of processes, this embedding can be efficiently implemented via state transition and holding time operators. Right: This method can efficiently reduce not only qubits number but also circuit depth.

Popular summary

In the realm of physics, tackling complex continuous-time stochastic processes has long been a challenge due to the lack of analytic solutions and the formidable computational consumption of numerical methods. However, this research proposes a new quantum algorithmic framework offering a game-changing solution. This framework consists of two crucial components: data preparation and information extraction. Data preparation reduces time and space complexity by statistics-inspired information compression. It can also be used in other quantum algorithms, addressing data input bottlenecks. Information extraction processes this compressed data with quadratic acceleration, expanding the quantum-enhanced Monte Carlo method. The impact is far-reaching, with applications in statistics, physics, time series analysis, and finance. Examples include option pricing and ruin probability calculation, showcasing its ability to handle extreme market events and history-dependent data. In essence, this quantum algorithmic framework provides a powerful tool for a more accurate analysis of stochastic phenomena.

► BibTeX data

@article{Zhuang2023quantumencoding,
  doi = {10.22331/q-2023-10-03-1127},
  url = {https://doi.org/10.22331/q-2023-10-03-1127},
  title = {Quantum {E}ncoding and {A}nalysis on {C}ontinuous {T}ime {S}tochastic {P}rocess with {F}inancial {A}pplications},
  author = {Zhuang, Xi-Ning and Chen, Zhao-Yun and Xue, Cheng and Wu, Yu-Chun and Guo, Guo-Ping},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {7},
  pages = {1127},
  month = oct,
  year = {2023}
}

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[1] Yewei Yuan, Chao Wang, Bei Wang, Zhao-Yun Chen, Meng-Han Dou, Yu-Chun Wu, and Guo-Ping Guo, "An improved QFT-based quantum comparator and extended modular arithmetic using one ancilla qubit", New Journal of Physics 25 10, 103011 (2023).

[2] Sascha Wilkens and Joe Moorhouse, "Quantum computing for financial risk measurement", Quantum Information Processing 22 1, 51 (2023).

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