The stock phrase that a quantum computer tries every possibility at once falls apart at the end: n qubits really do carry 2ⁿ amplitudes, but a measurement returns exactly one outcome, with probability equal to the squared amplitude, so an algorithm has to funnel amplitude onto the answer before measuring. A Hadamard gate takes |0⟩ to (|0⟩+|1⟩)/√2, swinging the state from the north pole of the Bloch sphere out to the equator; add CNOT and the two qubits become a Bell pair (|00⟩+|11⟩)/√2, perfectly correlated yet still unable to signal faster than light. The advantage exists only for a few problems such as Shor and Grover.
The stock phrase that a quantum computer tries every possibility at once falls apart at the end: n qubits really do carry 2ⁿ amplitudes, but a measurement returns exactly one outcome, with probability equal to the squared amplitude, so an algorithm has to funnel amplitude onto the answer before measuring. A Hadamard gate takes |0⟩ to (|0⟩+|1⟩)/√2, swinging the state from the north pole of the Bloch sphere out to the equator; add CNOT and the two qubits become a Bell pair (|00⟩+|11⟩)/√2, perfectly correlated yet still unable to signal faster than light. The advantage exists only for a few problems such as Shor and Grover.
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