11.2 Quantum searching via Grover

So how can we do better than looking at every one of n items in an unordered collection? If we had ten classical systems, we could divide the collection ten ways and search each chunk. This process is still O(n) because the time is still proportional to the collection’s size. We would also be adding overhead to parallelize the search over multiple systems.

The remainder of this chapter shows the basic ideas of how the Grover search algorithm finds the result in O(√n) time. [GSA] The detailed mathematics of the algorithm is well described elsewhere.

I cover the Grover search algorithm in sections 9.5 through 9.7 of Dancing with Qubits. [DWQ]

Suppose I have a box of 8 dimmable light bulbs. They are all distinct in some way so that I can tell them apart. I number them 0 through 7, or, in binary, 000 through 111. Even better, I label...