Self-Improving Quantum Search: Using Grover's Algorithm to Discover Superior Algorithms

We propose a framework for algorithmic self-improvement based on quantum search. The core idea is to use Grover’s algorithm to search the space of quantum algorithms for one that outperforms Grover itself. The discovered algorithm then searches for an even better algorithm, and so on. We formalize this recursive improvement process and analyze the conditions under which it converges to optimal query complexity.