Quantum Computing Asked on December 21, 2020
The documentation for the new version Qiskit 0.20.0 states that:
$U(θ,ϕ,λ)=RZ(ϕ−π/2)RX(π/2)RZ(π−θ)RX(π/2)RZ(λ−π/2)$"
$U3(θ,ϕ,λ)=RZ(ϕ)RX(−π/2)RZ(θ)RX(π/2)RZ(λ)$"
It looks like only the latter matches the known rotation sequence for U3:
$z$-rotation ($lambda$), $y$-rotation ($theta$), $z$-rotation ($varphi$)
Although their presentation matrices completely coincide:
$$
mathrm{U3}=
mathrm{U}=
begin{pmatrix}
cos(theta/2) & -mathrm{e}^{ilambda}sin(theta/2)
mathrm{e}^{iphi}sin(theta/2) & mathrm{e}^{i(phi+lambda)}cos(theta/2)
end{pmatrix}.
$$
Is this an inaccuracy in the documentation or am I missing something and these gates are actually different?
Just in case, the aforementioned difference stated in the documentation refers to the hardware (not software) implementation of these gates on IBM Q systems.
If you look at the source code then you will see that the UGate
is defined as an alias for the U3Gate
. As to why do they need this alias, I do not know for sure. But if I were to hazard a guess, then it would be because in most quantum computing literature, $U$ is used to refer to an arbitrary unitary gate/operator. Since in qiskit U3Gate
is the most generic single qubit unitary gate, it makes sense to identify it with $U$ from quantum computing literature.
Answered by e-eight on December 21, 2020
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