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by codekilla 3059 days ago
This is verbatim from 'Explorations in Quantum Computing' by Colin P. Williams: "The utility of the Hadamard gate derives from that fact that by applying, in parallel, a separate Hadamard gate to each of n qubits, each initially in the state |0⟩, 1 H|0⟩⊗H|0⟩⊗···⊗H|0⟩= √ |j⟩ (2.20)

we can create an n-qubit superposition containing 2n component eigenstates. These eigenstates represent all the possible bit strings one can write using n bits. The importance of this capability is often overlooked. But, in reality, it is one of the most important tricks of quantum computing as it gives is the ability to load exponentially many indices into a quantum computer using only polynomially many operations. Had Nature been unkind, and had we had to enter the different bit-strings individually, as we do in classical computing, then quantum computing would have had far less potential for breakthroughs in computational complexity."

I'm just talking about loading a quantum register, there are other issues with gate times and decoherence.