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Checking if a set of quantum gates is universal can be done using group theory methods [18] and/or relation to (approximate) unitary t-designs [19] Some universal quantum gate sets include: The rotation operators R x (θ), R y (θ), R z (θ), the phase shift gate P(φ) [c] and CNOT are commonly used to form a universal quantum gate set. [20] [d]
In gate-based quantum computing, various sets of quantum logic gates are commonly used to express quantum operations. The following tables list several unitary quantum logic gates, together with their common name, how they are represented, and some of their properties.
The Toffoli gate can be realized by five two-qubit quantum gates, [5] but it can be shown that it is not possible using fewer than five. [6] Another universal gate, the Deutsch gate, can be realized by five optical pulses with neutral atoms. [7] The Deutsch gate is a universal gate for quantum computing. [8]
Other examples of quantum logic gates derived from classical ones are the Toffoli gate and the Fredkin gate. However, the Hilbert-space structure of the qubits permits many quantum gates that are not induced by classical ones. For example, a relative phase shift is a 1 qubit gate given by multiplication by the phase shift operator:
The classical analog of the CNOT gate is a reversible XOR gate. How the CNOT gate can be used (with Hadamard gates) in a computation.. In computer science, the controlled NOT gate (also C-NOT or CNOT), controlled-X gate, controlled-bit-flip gate, Feynman gate or controlled Pauli-X is a quantum logic gate that is an essential component in the construction of a gate-based quantum computer.
Quantum gate teleportation; T. Toffoli gate This page was last edited on 31 December 2018, at 21:28 (UTC). Text is available under the Creative Commons ...
a fixed but arbitrary list of static gates (quantum gates that do not depend on parameters, like the Hadamard gate.) ′ a fixed but arbitrary list of parametric gates (gates that depend on a number of complex parameters like the phase shift gate that requires an angle parameter to be completely defined.)