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In this paper we provide a quantum Monte Carlo algorithm to solvehigh-dimensional Black-Scholes PDEs with correlation for high-dimensionaloption pricing. The payoff function of the option is of general form and isonly required to be continuous and piece-wise affine (CPWA), which covers mostof the relevant payoff functions used in finance. We provide a rigorous erroranalysis and complexity analysis of our algorithm. In particular, we prove thatthe computational complexity of our algorithm is bounded polynomially in thespace dimension $d$ of the PDE and the reciprocal of the prescribed accuracy$\varepsilon$ and so demonstrate that our quantum Monte Carlo algorithm doesnot suffer from the curse of dimensionality.

Quantum Monte Carlo algorithm for solving Black-Scholes PDEs for  high-dimensional option pricing in finance and its proof of overcoming the  curse of dimensionality