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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]
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.
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 Clifford gates do not form a universal set of quantum gates as some gates outside the Clifford group cannot be arbitrarily approximated with a finite set of operations. An example is the phase shift gate (historically known as the π / 8 {\displaystyle \pi /8} gate):
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.
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In the quantum mechanics study of optical phase space, the displacement operator for one mode is the shift operator in quantum optics, ^ = (^ † ^), where is the amount of displacement in optical phase space, is the complex conjugate of that displacement, and ^ and ^ † are the lowering and raising operators, respectively.
Arbitrary Clifford group element can be generated as a circuit with no more than (/ ()) gates. [6] [7] Here, reference [6] reports an 11-stage decomposition -H-C-P-C-P-C-H-P-C-P-C-, where H, C, and P stand for computational stages using Hadamard, CNOT, and Phase gates, respectively, and reference [7] shows that the CNOT stage can be implemented using (/ ()) gates (stages -H- and -P ...