Discovery of Quantum Algorithms Using Genetic Algorithms: Exponential Speedup via Random Sampling

The integration of classical machine learning with quantum computing is a promising frontier for solving complex problems more efficiently. This study focuses on discovering oracle-based quantum algorithms, specifically quantum search algorithms like Grover's algorithm, using genetic algorithms (GAs). By leveraging random sampling of oracle combinations, our method reduces the evaluation time complexity from <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{O}(2^{\mathrm{n}})$</tex> to O(n), enabling the efficient optimization of larger n-qubit circuits. The fitness evaluation of quantum circuits was based on a reduced number of random oracle combinations, significantly speeding up the process while maintaining optimization effectiveness. Our GA experiments, involving up to 8-qubit oracles, demonstrated the ability to identify the first iteration of Grover's algorithm and provided insights into the algorithm's performance across various circuit sizes. The results highlight the efficacy of our fast evaluation method in accelerating classical optimization techniques for discovering quantum algorithms, offering a scalable solution for larger qubit configurations. Limitations and potential improvements for handling even larger qubit sizes are also discussed.