Leveraging Quantum Computing and Optimization to Estimate Financial Crashes in Small and Medium-Sized Enterprises

In this study, we focus on estimating financial crashes within a network of small and medium enterprises (SMEs) that are customers of Yapi Kredi Bank. These SMEs have complex financial relationships involving receivables and payables among each other. We developed a quadratically constrained quadratic program as a mathematical optimization model aiming at identifying significant vulnerabilities and potential failure points in this network. By defining key parameters such as crossholding ratios, self-holding fractions, asset ownership proportions, and failure cost functions, we capture the intricate dependencies between these entities. The model is inherently nonlinear due to the quadratic terms and constraints, reflecting the real-world complexities of financial networks. Solving this NP-hard problem using classical methods is challenging; therefore, we leverage quantum computing technology to efficiently explore the solution space and produce decision variables that indicate the likelihood of financial distress for each SME in the network. The difficulty of this problem lies in the potential domino effect, where a single delayed payment can trigger subsequent financial distress among connected entities, leading to a cascading collapse within the financial network. Classical computing solutions for such problems would take an impractical amount of time, estimated at 13.7 billion years. In contrast, using quantum computing, our optimization model solves the problem in approximately 7 seconds. Using financial data from 2019, our model successfully identified 90.04 million TL out of 107 million TL of non-performing loans. Similarly, using data from 2020, it identified 669.92 million TL out of 726 million TL of non-performing loans. Overall, the model accurately predicted 91.2.