Quantum computing
= Quantum computing
{wiki}
= Quantum computation
{synonym}
<Quantum computing> processes <quantum information> through controlled physical transformations and <quantum measurements>. In the <quantum circuit> model, an initial <quantum state> evolves through <quantum gates>, and the <Born rule> predicts the final outcome probabilities. <Quantum interference> makes the relative <quantum phases> of amplitudes computationally useful. <David Deutsch>'s 1985 paper developed a model of universal <quantum computation>.<Quantum theory, the Church-Turing principle and the universal quantum computer by David Deutsch>[Sections 2–3, quantum computation and universal quantum computers]{ref}
A one-<qubit> example shows why amplitudes matter. Starting from $|0\rangle$, a <Hadamard gate> gives $(|0\rangle+|1\rangle)/\sqrt2$; a second <Hadamard gate> returns $|0\rangle$. Insert a <Pauli Z gate> between the two <Hadamard gates> and the final state is instead $|1\rangle$: the intermediate relative sign changes how amplitudes combine. Measuring the intermediate state alone would give equal probabilities in both cases. A useful <quantum algorithm> arranges such transformations to make information about the required answer accessible through the final <quantum measurement>.