U1Gate¶

class U1Gate(theta, label=None)[source]¶

Bases: Gate

Single-qubit rotation about the Z axis.

This is a diagonal gate. It can be implemented virtually in hardware via framechanges (i.e. at zero error and duration).

Warning

This gate is deprecated. Instead, the following replacements should be used

\[U1(\lambda) = P(\lambda)= U(0,0,\lambda)\]

circuit = QuantumCircuit(1)
circuit.p(lambda, 0) # or circuit.u(0, 0, lambda)

Circuit symbol:

     ┌───────┐
q_0: ┤ U1(λ) ├
     └───────┘

Matrix Representation:

\[\begin{split}U1(\lambda) = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\lambda} \end{pmatrix}\end{split}\]

Examples:

\[U1(\lambda = \pi) = Z\]

\[U1(\lambda = \pi/2) = S\]

\[U1(\lambda = \pi/4) = T\]

See also

RZGate: This gate is equivalent to RZ up to a phase factor.

\[U1(\lambda) = e^{i{\lambda}/2} RZ(\lambda)\]

U3Gate: U3 is a generalization of U2 that covers all single-qubit rotations, using two X90 pulses.

Reference for virtual Z gate implementation: 1612.00858

Create new U1 gate.

Methods Defined Here

`control`	Return a (multi-)controlled-U1 gate.
`inverse`	Return inverted U1 gate (\(U1(\lambda)^{\dagger} = U1(-\lambda)\))

Attributes

decompositions¶: Get the decompositions of the instruction from the SessionEquivalenceLibrary.