Quantum Circuits for the Black-Scholes equations via Schrödingerisation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913825316405248 |
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| author | Jin, Shi Tang, Zihao Yin, Xu Zhang, Lei |
| author_facet | Jin, Shi Tang, Zihao Yin, Xu Zhang, Lei |
| contents | In this paper, we construct quantum circuits for the Black-Scholes equations, a cornerstone of financial modeling, based on a quantum algorithm that overcome the cure of high dimensionality. Our approach leverages the Schrödingerisation technique, which converts linear partial and ordinary differential equations with non-unitary dynamics into a system evolved by unitary dynamics. This is achieved through a warped phase transformation that lifts the problem into a higher-dimensional space, enabling the simulation of the Black-Scholes equation on a quantum computer. We will conduct a thorough complexity analysis to highlight the quantum advantages of our approach compared to existing algorithms. The effectiveness of our quantum circuit is substantiated through extensive numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04304 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Circuits for the Black-Scholes equations via Schrödingerisation Jin, Shi Tang, Zihao Yin, Xu Zhang, Lei Quantum Physics Numerical Analysis In this paper, we construct quantum circuits for the Black-Scholes equations, a cornerstone of financial modeling, based on a quantum algorithm that overcome the cure of high dimensionality. Our approach leverages the Schrödingerisation technique, which converts linear partial and ordinary differential equations with non-unitary dynamics into a system evolved by unitary dynamics. This is achieved through a warped phase transformation that lifts the problem into a higher-dimensional space, enabling the simulation of the Black-Scholes equation on a quantum computer. We will conduct a thorough complexity analysis to highlight the quantum advantages of our approach compared to existing algorithms. The effectiveness of our quantum circuit is substantiated through extensive numerical experiments. |
| title | Quantum Circuits for the Black-Scholes equations via Schrödingerisation |
| topic | Quantum Physics Numerical Analysis |
| url | https://arxiv.org/abs/2505.04304 |