Hybrid Quantum-Classical Algorithms

This thesis explores hybrid algorithms that combine classical and quantum computing to enhance the performance of classical algorithms. Two approaches are studied: a hybrid search and sample optimization algorithm and a classical algorithm that assesses the cost and performance of quantum algorithms in chemistry. Hybrid algorithms are vital due to limitations in both classical and quantum computing, offering a solution by leveraging the strengths of both. The first algorithm, quantum Metropolis Solver (QMS), adapts a quantum walk to a Metropolis-Hastings algorithm for industrial applications, demonstrating advantages over classical counterparts in various sectors. The second algorithm, TFermion, is a classical tool for evaluating the cost of T-type gates in quantum chemistry algorithms, aiding in the comparison and execution of these algorithms on real quantum hardware, and applied to the design of more efficient electric batteries.