Scotland-Korea Collaboration on quantum simulation in asset pricing based on the quantum harmonic oscillator

This proposal brings together researchers from Glasgow Caledonian University and Yonsei University in South Korea to tackle computational challenges in quantum finance using quantum computing. Specifically, the project focuses on improving the computational efficiency of the Quantum Harmonic Oscillator (QHO) model for modelling asset return distributions, employing quantum simulations to better explain the dynamics of financial markets.
In the QHO model, the probability assigned to each excited state can capture the normality, skewness, and kurtosis of return distributions. Moreover, the QHO model is free from strict conditions, such as the assumption of normality, and has a more precise capability to examine the efficient market hypothesis compared to traditional econometric methods, such as variance ratio tests. Despite the QHO model’s solid theoretical foundation, computational bottlenecks can hinder its broader application in practical implementations. Since the closed-form solution involves a linear combination of an infinite number of χ-distributions, the calculation requires substantial computing resources to fully capture the state information. Therefore, the empirical application requires significant truncation to obtain feasible results in classical computations, which may limit precision by omitting higher excited states.
These challenges stem from the substantial computational costs that increase exponentially with the number of parameters considered, making it impractical to extend beyond a few excited states. To address this, the project aims to develop a quantum computing algorithm and/or QHO-based framework to optimise computational resources and improve precision over classical computing. By encoding the QHO model into quantum circuits, the project seeks to leverage quantum algorithms, such as the quantum Monte Carlo method, to improve computational efficiency in estimating model parameters. This project is expected to advance both quantum finance and quantum computing by providing a more accurate and efficient tool for asset pricing and a practical application of quantum computing.