Hybrid classical-quantum computing: Applications to statistical mechanics of financial markets

Abstract

Hybrid Classical-Quantum computing is now offered by several commercial quantum computers. In this project, a model of financial options, Statistical Mechanics of Financial Markets (SMFM), uses this approach. However, only Classical (super-)computers are used to include the quantum features of these models. Since 1989, Adaptive Simulated Annealing (ASA), an optimization code using importance-sampling, has fit parameters in such models. Since 2015, PATHINT, a path-integral numerical agorithm, has been used to describe several systems in several disciplines. PATHINT has been generalized from 1 dimension to N dimensions, and from classical to quantum systems into qPATHINT. Published papers have described the use of qPATHINT to neocortical interactions and financial options. The classical space modeled by SMFM fits parameters in conditional short-time probability distributions of nonlinear nonequilibrium multivariate statistical mechanics, while the quantum space modeled by qPATHINT describes quantum money. This project demonstrates how some hybrid classical-quantum systems may be calculated using only classical (super-)computers.