Epilogue – what does have to do with Grover’s algorithm?
When you run Grover’s algorithm, the optimal number of iterations is , where is the number of things you’re searching through. In this formula, you have qubits and .
Usually, the formula requires a few tweaks. For example, you can’t use the formula to search through exactly 1,000 items, because 1,000 isn’t a power of 2. Instead, you add 24 fake items to your list. Then, you use 10 qubits to search through items. And what if isn’t an integer? The value of is approximately 25.1327, and you can’t apply the Grover iterate 25.1327 times. In this case, there are ways to decide whether Grover’s sweet spot is 25 or 26, but we won’t get into that here.
In this section, our goal is to convey some idea of the role plays in the number of Grover iterate applications. Our explanation has many gaps and involves several approximations. We won’t come to...