Controlled NOT gate using multiple control qubits in Q#

Question

I am trying to implement the Grover's search algorithm using Q# and I am not able to implement the oracle (black box) part for the search of state $|1010\rangle$. How to implement the controlled NOT gate using 5 qubits with 4 qubits (q[0] ... q[3]) used as the control qubits and q[4] as the target qubit in Q#?

Please correct me if this is wrong, I am trying to implement Grover's algorithm using 4 qubits where 3 qubits are for the states and the 4th qubit is the auxiliary qubit so the auxiliary bit should be the target qubit?

Answer 1

You can implement a controlled version of any gate in Q# using Controlled functor; for the oracles, you'll use something like Controlled X(controlQubits, targetQubit), where controlQubits is an array of qubits that have to be in 1 state for the X gate to be applied and targetQubit is the qubit to which the gate is applied.

Q# also has a neat library function ControlledOnBitString which allows to apply controlled version of the gate if the control qubits are in a state given by the bit string. So if you want to encode a specific state to use as control, like $|1010\rangle$ in your example, you can use

(ControlledOnBitString([true, false, true, false], X))(controlQubits, targetQubit);

You can see examples of implementing Grover's search using Q# in the GroverSearch kata (task 1.2 is almost exactly your example of looking for a state 1010).