Quantum Computing for Financial Mathematics

Belal Ehsan Baaquie

Dylan Herman, Cody Googin, Xiaoyuan Liu +5 more

S. Rajagopalan, T Mohana Sundari, M. Gayathri

Quantum computing is an emerging area of computer science that combines computing, physics and mathematics to solve the real-time problems of industry, economy and operations. It is a multidisciplinary approach that applies computing technologies in the various operations of the economy to achieve comprehensive quality management. Financial planning and control is an integral part of financial management that is very crucial for any enterprise whether it is profit oriented or not. Financial management started using computing technologies in analysis and decision- making. Financial management has to deal with large amounts of data which is easily done with the help of Quantum computing methodology. Companies can also use quantum computing to empower customers to experience better financial services. It takes consumer behaviours as inputs in order to predict the needs in real-time and near future. Major financial institutions and companies such as JP Morgan Chase, HSBC, Goldman Sachs, etc. started using quantum computing for their financial operations and decisions. In future, almost all industries will have the real-time application of quantum computing in their operations at a micro or macro level.

Pablo Herrero-Gómez, Francisco A. Pujol, Ana Martinez García +1 more

Pragnesh B. Dalwadi

Quantum computing is set to transform various industries. Among them, the financial sector is especially vulnerable due to its reliance on encryption for securing transactions, customer data and proprietary financial models. Quantum computing threatens financial institutions by breaking current cryptographic methods, making them more vulnerable than other industries. This paper examines the potential impact of quantum computing on financial data security and focuses on the challenges and opportunities it presents. Quantum computers can solve complex mathematical problems more efficiently than classical computers. They pose a significant threat to current cryptographic systems that safeguard financial data. To mitigate this risk, financial institutions must adopt quantum-resistant encryption to maintain data integrity and privacy. On the other hand, quantum computing offers opportunities for enhancing financial security through advanced algorithms and improved risk assessment models. The paper also explores ethical and regulatory considerations, emphasizing the need for proactive measures to align technological advancements with societal values and legal frameworks. Addressing these challenges while leveraging opportunities will enable the financial industry to navigate the quantum era securely.

Román Orús, Samuel Mugel, Enrique Lizaso

A key problem in financial mathematics is the forecasting of financial crashes: If we perturb asset prices, will financial institutions fail on a massive scale? This was recently shown to be a computationally intractable (NP-hard) problem. Financial crashes are inherently difficult to predict, even for a regulator which has complete information about the financial system. In this Rapid Communication, we show how this problem can be handled by quantum annealers. More specifically, we map the equilibrium condition of a toy-model financial network to the ground-state problem of a spin-1/2 quantum Hamiltonian with two-body interactions, i.e., a quadratic unconstrained binary optimization problem. The equilibrium market values of institutions after a sudden shock to the network can then be calculated via adiabatic quantum computation and, more generically, by quantum annealers. Our procedure could be implemented on near-term quantum processors, thus providing a potentially more efficient way to assess financial equilibrium and predict financial crashes.