Optimized Quantum Circuit Implementation of Payoff Function
Sejin Lim, Hyunjun Kim, Kyungbae Jang, Siyi Wang, Anubhab Baksi, Anupam Chattopadhyay, Hwajeong Seo · 2023
Large-scale quantum computers that can execute practical quantum algorithms have the potential to solve complex problems that are currently challenging for classical computers. This involves converting these problems into a form that can be processed by quantum circuits, a crucial process that requires minimizing quantum resources like qubit count, gate count, and circuit depth. Our work focuses on implementing and optimizing the foundational task of quantum finance, known as option pricing, as a quantum circuit. This enables the utilization of quantum computing benefits, within the financial domain. Specifically, we implement and optimize the function fK(S) = max(S−K, 0). Taking into consideration the significant trade-offs between qubit count and circuit depth, we have developed quantum circuits for the optimized implementation of the fK(S). Our work incorporates various optimization techniques for the circuit, such as selecting the optimal adder, optimizing the S−K operation, parallelization, and qubit reuse. Furthermore, we offer various versions of our quantum circuits for the fK(S), each featuring different adders and Toffoli decompositions, thereby providing flexibility for a wide range of use cases.