Time Complexity Analysis - DJ

We'll go through the mathematical proof to understand why the DJ algorithm works in the first place.


Our qubits are initialized to the 0|0\rangle state and we also have an extra qubit, ancilla, that is initialized to the 1|1\rangle state using an XX gate. The current quantum state of our qubits can be represented as follows:

ψ0=00...01=0n1|\psi_0\rangle = |00...0\rangle \otimes|1\rangle= |0\rangle^{\otimes n} \otimes|1\rangle

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