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Quantum-inspired variational algorithms for partial differential equations: Application to financial derivative pricing (2207.10838v1)
Published 22 Jul 2022 in math.NA, cs.NA, and q-fin.MF
Abstract: Variational quantum Monte Carlo (VMC) combined with neural-network quantum states offers a novel angle of attack on the curse-of-dimensionality encountered in a particular class of partial differential equations (PDEs); namely, the real- and imaginary time-dependent Schr\"odinger equation. In this paper, we present a simple generalization of VMC applicable to arbitrary time-dependent PDEs, showcasing the technique in the multi-asset Black-Scholes PDE for pricing European options contingent on many correlated underlying assets.