Quantum Circuits for the Black-Scholes equations via Schrödingerisation

• URL: http://arxiv.org/abs/2505.04304v1
• Date: Wed, 07 May 2025 10:21:12 GMT
• Title: Quantum Circuits for the Black-Scholes equations via Schrödingerisation
• Authors: Shi Jin, Zihao Tang, Xu Yin, Lei Zhang,
• Abstract summary: We construct quantum circuits for the Black-Scholes equations.<n>We will conduct a thorough complexity analysis to highlight the quantum advantages of our approach.
• Score: 26.57843095806779
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 Schr\"odingerisation 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.

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