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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] The Clifford set {CNOT, H, S} + T gate. The Clifford set alone is not a universal quantum gate set, as it can be efficiently simulated classically according to the Gottesman–Knill theorem.
Arbitrary single-qubit phase shift gates () are natively available for transmon quantum processors through timing of microwave control pulses. [13] It can be explained in terms of change of frame. [14] [15] As with any single qubit gate one can build a controlled version of the phase shift gate.
In quantum computing and quantum information theory, the Clifford gates are the elements of the Clifford group, ... An example is the phase shift gate ...
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:
It gives a nonlinear phase shift on one mode conditioned on two ancilla modes. Linear optics implementation of NS-gate. The elements framed in the box with dashed border is the linear optics implementation with three beam splitters and one phase shifter (see text for parameters). Modes 2 and 3 are ancilla modes.
The smallest global phase is +, the eighth complex root of the number 1, arising from the circuit identity = +, where is the Hadamard gate and is the Phase gate. For n = {\displaystyle n=} 1, 2, and 3, this group contains 24, 11,520, and 92,897,280 elements, respectively. [ 5 ]
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.)
In quantum computing, the quantum phase estimation algorithm is a quantum algorithm to estimate the phase corresponding to an eigenvalue of a given unitary operator.Because the eigenvalues of a unitary operator always have unit modulus, they are characterized by their phase, and therefore the algorithm can be equivalently described as retrieving either the phase or the eigenvalue itself.