> it improves the search time by approximately halving the number of items to be searched (i.e. AES-256 is reduced to 128 bits of security, AES-128 is reduced to 64, etc).

No, "halving the number of items to be searched" would be a constant factor (1/2) change, which would be trivial. Computers get that much faster in a year.

Rather, using Grover brute search to crack a hash reduces the effective number of items to try by a square root. Each bit of AES increases cracking time by a factor of 2, which is why decreasing the cracking time by a square root is equivalent to halving the number of bits of security: sqrt(2^N) = 2^(N/2)