Get Minimum Binary Value from Arbitrary Blackbox Oracle Result

Question

Suppose there are three quantum registers and one classical register.

1. Operand A: 3-qubit
2. Operand B: 3-qubit
3. Results C: 6-qubit
4. Results D: 6-bit

The operand A is deterministic (user input), and the operand B is bruteforcer, while the result C is output buffer.

Since A is user input, the bit initializer is just using NOT gate depends on user preference.

In another hand, B is bruteforcer which the bit initializer is Hadamard gate that setted up for all qubits (3-qubit).

Suppose there is blackbox oracle (operator) that receive both operands as inputs and returning 6-qubit.

How do I get the highest probability of minimum binary value from such 6-qubit output that will be stored in 6-bit classical register (through measurement)?

We know that, minimum binary value of 6-qubit is |000000>, but is it the highest probability?

Answer 1

You can mark the solution state, e.g. $|000000 \rangle$, by an oracle and amplify an amplitude of that state by a diffusion operator in grover's algorithm. Apply a grover's iterator some times then you'll get a deserved state with a high probability.

For that example you mentioned in the comment below, you need to construct an oracle for your specific needs.

If you want to amplify a state under 5 just make an oracle doing it. Since you have 6-qubits for input, an oracle marks a state such that upper 3-qubits of input are always zero and a condition NOT('111' or '110' or '101) meets for the lower 3-qubits.

Finally, an oracle and a diffuser doing that all would look like this :

Plus, the result looks like this :

As you see only those states below 5 have higher probability than others.