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.
Highlights
There are several companies offering commercial-grade Hybrid Classical-Quantum computers that can be accessed via the Cloud, e.g., Rigetti, D-Wave, Microsoft, and IBM [1]; see https://docs.ocean.dwavesys.com/projects/hybrid/en/latest/index.html https://www.rigetti.com/what https://azure.microsoft.com/en-us/solutions/hybrid-cloud-app/#overview https://www.ibm.com/it-infrastructure/z/capabilities/hybrid-cloud These companies typically offer Hybrid computing, consisting of Classical computers to run optimization program on parameters in systems that are described by quantum variables using their Quantum computers [2], Some studies show Quantum computing is still not possible for many systems, even with classical optimizers [3]
Quantum computing is rapidly growing, which will be applied in many ways to financial markets
Financial markets will be expanded to include quantum variables; financial markets will determine how Quantum Money (QM) is to be valued and how it may be exchanged with current financial instruments
Summary
There are several companies offering commercial-grade Hybrid Classical-Quantum computers that can be accessed via the Cloud, e.g., Rigetti, D-Wave, Microsoft, and IBM [1]; see https://docs.ocean.dwavesys.com/projects/hybrid/en/latest/index.html https://www.rigetti.com/what https://azure.microsoft.com/en-us/solutions/hybrid-cloud-app/#overview https://www.ibm.com/it-infrastructure/z/capabilities/hybrid-cloud These companies typically offer Hybrid computing, consisting of Classical computers to run optimization program on parameters in systems that are described by quantum variables using their Quantum computers [2], Some studies show Quantum computing is still not possible for many systems, even with classical optimizers [3]. These codes run on Classical computers, defining a Hybrid Classical-Quantum solely on a Classical computer. As with today’s technologies, probability distributions of prices in real markets will not generally be simple Gaussian or log-normal distributions that yield closed form options solutions. More details on how hybrid quantum-classical computing is being applied to this system currently is in another companion paper [20]
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