In the Deutsch-Jozsa algorithm, the Hadamard gates create a superposition of all possible input states. The oracle gate then applies the function f to the input qubits, effectively encoding the function into the quantum state. The second set of Hadamard gates then "uncompute" the superposition, leaving the input qubits in a state that can be measured to determine the nature of the function f.

For a constant function, the output of the oracle gate will be the same for both input bit strings, resulting in a final state that is either |00⟩ or |11⟩. When the input qubits are measured, the result will always be the same, indicating that the function is constant.

For a balanced function, the output of the oracle gate will be different for the two input bit strings, resulting in a final state that is a superposition of all possible output states. When the input qubits are measured, the result will be one of the possible 2-bit strings other than |00⟩ or |11⟩, indicating that the function is balanced.

Well, as you probably already know, Quantum Computers have the ability to perform exponentially faster than classical computers for certain specific tasks. And when it comes to solving problems from areas like number theory, codebreaking or database search problems that take a lot of time and resources using classical computational approach to arrive at the answer can be simplified in feasible time using quantum probabilistic models.

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