Lloyds develops quantum algorithms for linear PDES arising in Finance

Executive Summary

On Dec 2019, researchers at Lloyds and Imperial College published an research article on hybrid quantum-classical algorithm to price European and Asian options. The authors do so by mapping the Black-Scholes model into the Schrodinger equation – the central equation in quantum mechanics. The authors then run numerical proof-of-concept experiments by simulating a 4-qubit quantum computer on a classical computer.

Our opinions

Pricing financial derivatives are important problems in quantitative finance that cannot be solved efficiently by a classical computer. With a fault-tolerant quantum computer, linear PDES such as the Black-Scholes model can be efficiently solved by the celebrated quantum algorithm known as HHL. However, such machine is still far reaching.

In this paper, the authors devise a quantum algorithm for near-term quantum devices to tackle the Black-Scholes model in a scaled-down scenario. Similar to other state-of-the-art works, such algorithm can accommodate certain levels of noise in real quantum devices but still lack of mathematical proof of their quantum advantage, unlike the HHL algorithm. To reach the real-world application, both quantum software and hardware have to be improved. Nevertheless, this paper opens an exciting direction for further research on the use of quantum computing for quantitative finance.