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For example we have state on input: <math>|0, 0, 1,1,0, 1\rang</math>. Last qubit is answer qubits. So on output we will have: <math>|0, 0, 1,1,0, 1\oplus 0\oplus 0\oplus 1\oplus 1\oplus 0\rang=|0, 0, 1,1,0, 1\rang</math>. Last qubit don't change value, and is 1, so function is balanced.
Becouse i don't know what gate is used in Deutsch-Jozsa algorithm or toffoli gate or Controlled-U gate? What is <math>U_f</math>? Tofoli gate or controlled-U gate? If controlled-U gate, then why last qubit dont go trough Hadamard gate and why measuring is first qubits, bet not last one? If there is Controlled-U gate (where is one controlled qubit and n target qubits (in toffoli gate is n controlled qubits and 1 target)) then it is explain why measuring is last qubit, but why need first qubits then pass at last step trough Hadamard gates?
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