Home banking and digital payments diffusion has greatly increased in recent years. As a result, fraud has also dramatically grown, resulting in the loss of billions of dollars worldwide every year. Therefore, banks and financial institutions are required to offer clients increasingly effective and sophisticated services for illegal transaction detection. Machine learning strategies are commonly employed for this crucial application. However, classical models are not satisfactory enough in highly unbalanced classification tasks like fraud detection. Quantum machine learning, working intrinsically in a higher dimensional computation space thanks to superposition and entanglement, can express more complex models than its classical counterpart and thus could provide a significant advantage in identifying potential illegal transactions. This work aims to analyze the potential of quantum classifiers in the fraud detection context, focusing on the Variational Quantum Circuit (VQC) model. The study has been led by exploiting a dataset based on real transactions provided by Intesa Sanpaolo of 500000 items with 15 features. Considering the limitations of contemporary Noisy Intermediate-Scale Quantum (NISQ) computers and quantum simulators, the dataset has been reduced in the number of transactions and features, exploiting Principal Component Analysis (PCA). The results obtained have been compared on equal terms with those of the most commonly employed classical methods, such as Logistic Regression, Random Forest, XGBoost, Support Vector Machine, and Neural Networks, obtaining a better classification quality in terms of recall. Even though this work is preliminary, the results are encouraging and prove the quantum models’ potential in highly unbalanced classification tasks.

Optimization is a crucial challenge across various domains, including finance, resource allocation, and mobility. Quantum computing has the potential to redefine the way we handle complex problems by reducing computational complexity and enhancing solution quality. Optimization, particularly of objective functions, stands to benefit significantly from quantum solvers, which leverage principles of quantum mechanics like superposition, entanglement, and tunneling. The Ising and Quadratic Unconstrained Binary Optimization (QUBO) models are the most suitable formulations for these solvers, involving binary variables and constraints treated as penalties within the overall objective function. To harness quantum approaches for optimization, two primary strategies are employed: exploiting quantum annealers—special-purpose optimization devices—and designing algorithms based on quantum circuits. This review provides a comprehensive overview of quantum optimization methods, examining their advantages, challenges, and limitations. It demonstrates their application to real-world scenarios and outlines the steps to convert generic optimization problems into quantum-compliant models. Lastly, it discusses available tools and frameworks that facilitate the exploration of quantum solutions for optimization tasks.

Simulated Quantum Annealing (SQA) is a heuristic algorithm which can solve Quadratic Unconstrained Binary Optimization (QUBO) problems by emulating the exploration of the solution space done by a quantum annealer. It mimics the quantum superposition and tunnelling effects through a set of correlated replicas of the spins system representing the problem to be solved and performing Monte Carlo steps. However, the effectiveness of SQA over a classical algorithm strictly depends on the cost/energy profile of the target problem. In fact, quantum annealing only performs well in exploring functions with high and narrow peaks, while classical annealing is better in overcoming flat and wide energy-profile barriers. Unfortunately, real-world problems have a heterogeneous solution space and the probability of success of each solver depends on the size of the energy profile region compatible with its exploration mechanism. Therefore, significant advantages could be obtained by exploiting hybrid solvers, which combine SQA and classical algorithms. This work proposes four new quantum-classical algorithms: Simulated Quantum Parallel Tempering (SQPT), Simulated Quantum Population Annealing (SQPA), Simulated Quantum Parallel Tempering - Population Annealing v1 (SQPTPA1) and Simulated Quantum Parallel Tempering - Population Annealing v2 (SQPTPA2). They are obtained by combining SQA, Parallel Tempering (PT), and Population Annealing (PA). Their results are compared with those provided by SQA, considering benchmark QUBO problems, characterized by different profiles. Even though this work is preliminary, the obtained results are encouraging and prove hybrid solvers’ potential in solving a generic optimization problem.

Quantum computers have the potential to solve Quadratic Unconstrained Binary Optimization (QUBO) problems with lower computational complexity than classical ones. Considering the current limitations of quantum hardware, the joint use of classical and quantum paradigms could exploit both advantages. Quantum routines can make some complex tasks for classical computers feasible. For example, in the Grover Adaptive Search (GAS) procedure, the problem cost function is classically shifted iteratively, whenever a negative value is found through the quantum Grover Search (GS) algorithm, until the minimum is achieved. This quantum-classical approach is characterized by many degrees of freedom, e.g. the number of GS iterations in each call and the stop condition of the algorithm, which should be appropriately tuned for an effective and fast convergence to the optimal solution. The availability of software routines could permit the best management of the GAS parameters. This work proposes new mechanisms for GAS parameters management and compares them with the existing ones, like one available in the Qiskit framework. The proposed mechanisms can automatically arrange the parameters according to the algorithm evolution and their previous experience, thus ensuring a more frequent and faster achievement of the optimal solution. Even though these strategies can be further improved, the results are encouraging. The analysis is done to identify the best policy for different problems. It lays the foundation for designing an automatic toolchain for QUBO solving, which can obtain the best possible implementation of the GAS algorithm for each submitted problem.