Working Paper Article Version 1 This version is not peer-reviewed

Hybrid Classical-Quantum Computing: Applications to Statistical Mechanics of Financial Markets

Version 1 : Received: 17 April 2021 / Approved: 19 April 2021 / Online: 19 April 2021 (09:09:32 CEST)

How to cite: Ingber, L. Hybrid Classical-Quantum Computing: Applications to Statistical Mechanics of Financial Markets. Preprints 2021, 2021040459 Ingber, L. Hybrid Classical-Quantum Computing: Applications to Statistical Mechanics of Financial Markets. Preprints 2021, 2021040459

Abstract

Hybrid Classical-Quantum computing has already arrived at several commercial quantum computers, offered to researchers and businesses. Here, applications are made to a model of financial options, Statistical Mechanics of Financial Markets (SMFM). These applications were published in many papers since the 1980's. This project only uses Classical (super-)computers to include quantum features of these models. Since 1989, an optimization code, Adaptive Simulated Annealing (ASA), has been to fit parameters in such models. Since 2015, a path-integral algorithm, PATHINT, used previously to accurately describe several systems in several disciplines, has been generalized from 1 dimension to N dimensions, and from classical to quantum systems, qPATHINT. Published papers have described the use of qPATHINT to neocortical interactions and financial options. The classical space by SMFM applies nonlinear nonequilibrium multivariate statistical mechanics to fit parameters in conditional short-time probability distributions, while the quantum space described by qPATHINT deals specifically with quantum systems, e.g., quantum money. This project thereby demonstrates how some hybrid classical-quantum systems may be calculated quite well using only classical (super-)computers.

Subject Areas

path integral; quantum systems; classical optimization; financial options

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