Regarding item number 2, can you create an example of a situation where quantum computing can more efficiently search a large database than a classical computer can?
Sure, let me give you an example.
Suppose you have a large database with N items, and you want to find a specific item within this database. A classical computer would need to check each item one by one, which would take O(N) time in the worst case.
In contrast, a quantum computer can use Grover's algorithm to search through the database in O(√N) time. This algorithm works by encoding the database into a quantum state, and then using a series of quantum operations to amplify the probability of finding the desired item.
The speedup of Grover's algorithm becomes more significant as the size of the database grows. For example, if you had a database with a billion items, a classical computer would need to check each item one by one, which could take hours or even days. In contrast, a quantum computer could potentially search the same database in just a few minutes using Grover's algorithm.
Note that this assumes an ideal quantum computer with perfect quantum gates and error correction. In reality, current quantum computers are still limited by noise and other sources of error, which can reduce the efficiency of quantum algorithms such as Grover's algorithm. Nonetheless, Grover's algorithm remains a powerful tool for searching large databases on a quantum computer.