How to find angle for Pauli-Z in U3

Question

What are the angles (lambda, phi and theta) for Pauli-Z gate in U3 ?

related: https://quantumcomputing.stackexchange.com/q/6236/55. If that doesn't answer your question, please provide more context and details (by editing the question accordingly, not in the comments). For example, what do you mean exactly with "find angle" here? — glS, Oct 31 '22 at 09:25

score 1 · Answer 1 · answered Nov 01 '22 at 08:05

1

You can use OneQubitEulerDecomposer class as follows:

from qiskit.circuit.library import ZGate
from qiskit.quantum_info import OneQubitEulerDecomposer
decomposer = OneQubitEulerDecomposer('U3')
theta, phi, _lambda = decomposer.angles(ZGate().to_matrix())
print(theta, phi, _lambda)

answered Nov 01 '22 at 08:05

Egretta.Thula

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I like this solution! – luciano Nov 01 '22 at 08:28

score 0 · Answer 2 · answered Oct 31 '22 at 11:19

You can turn rewrite your Pauli-Z into a U3 with transpile:

from qiskit import transpile
from qiskit.opflow import Z
circuit_u3 = transpile(Z.to_circuit(), basis_gates=['u3'])
circuit_u3.draw()

   ┌───────────┐
q: ┤ U3(0,0,π) ├
   └───────────┘

There you have the $\texttt{U3}(\theta, \phi, \lambda)$, $\theta=0$, $\phi=0$, and $\lambda=\pi$.

How to find angle for Pauli-Z in U3

2 Answers2