Description Of
Grover's algorithm requires a "quantum oracle" operator which can recognize solutions to the search problem and give them a negative sign. In order to keep the search algorithm general, we will leave the inner workings of the oracle as a black box, but will explain how the sign is flipped. The oracle contains a function which returns if is a solution to the search problem and otherwise. The oracle is a unitary operator which operates on two qubits, the index qubit and the oracle qubit :
As usual, denotes addition modulo 2. The operation flips the oracle qubit if and leaves it alone otherwise. In Grover's algorithm we want to flip the sign of the state if it labels a solution. This is achieved by setting the oracle qubit in the state, which is flipped to if is a solution:
We regard as flipped, thus the oracle qubit is not changed, so by convention the oracle qubits are usually not mentioned in the specification of Grover's algorithm. Thus the operation of the oracle is simply written as:
Read more about this topic: Grover's Algorithm
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