ObsidianVault/SS2026/Quantum Computing/16. Universal set of gates/Universal Set of Gates.md at 36fe24ab7a38fd888c32e4829a4afba1e27f118d

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Benjamin Neumann 36fe24ab7a vault backup: 2026-08-06 10:15:50

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A universal set of gates is a set of gates which is necessary to generate all possible gates. (Funktionale Menge basically (\land, \lnot))

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Pauli Gates

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But we can't create all gates from only Pauli matrices. For example, because we only manipulate a single qubit, we cant create the CNOT gate, which creates entanglement. And we cannot create all single-qubit gates from only pauli matrices either... because the product of pauli matrices is always a pauli matrix again or the identity..

Other Gates

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Rotation Gates

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Clifford Gates

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Gottesmann-Knill theorem

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