Researchers in the field of quantum computing have been working to determine where quantum algorithms can provide a speedup compared to classical algorithms. In 1994, Peter Shor developed a quantum algorithm for factoring large numbers, which classical computers struggle with due to the difficulty of the task. Lov Grover also found a quantum algorithm for a search problem, which was much faster than classical approaches. In the late 1990s, researchers explored the use of quantum algorithms for graph theory problems, and in 2002, a classically intractable search problem was identified that could be solved easily by a quantum algorithm. More recently, researchers have been developing algorithms that combine the benefits of quantum interference with memory, leading to potentially faster path-finding algorithms.
https://www.quantamagazine.org/to-move-fast-quantum-maze-solvers-must-forget-the-past-20230720/