Quantum Differential Machine Learning

The application of quantum computing to finance has become an increasingly active area of research. In this paper, we explore the expressive potential of quantum machine learning as an alternative to classical differential machine learning. Efficient computation of sensitivities remains the main issue in financial risk management and we discuss how parameter-shift rules used in gradient-based optimization of quantum machine learning help learning option prices and their sensitivities efficiently. The proposed method can be regarded as quantum analogous to classical differential machine learning, so we refer to it as quantum differential machine learning. Delta of European option and vega of Bermudan swaption as examples of learning in parametric space and delta of basket option as an example of learning in sample space are examined in numerical experiments. Our results show that our proposed method paves the way for using quantum machine learning for option pricing and sensitivity calculation in financial risk management.