Grovers algorithm for specific qubits

Question

Is it possible to use Grover's algorithm on a particular register instead of all qubits? For example, if I have the superposition of 2 qubits and I'm looking to see if qubit 1 is present on the second qubit, can I apply Grover's algorithm to increase the probabilities of 01 and 11 in the superposition of 2 qubits?

Answer 1

Yes, you can use Grover's search on a subset of qubits. Qubits used in a quantum algorithm are similar to variables in a classical program - you're not required to use all variables all the time, you can use a few to do one part of the calculation, and then use some of these and some of the others in another part.

Specifically for your example, though, Grover's search wouldn't be helpful: it does not work for cases when the solutions make up exactly one half of the search space.