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# U1Gate¶

class U1Gate(theta, label=None)[ソース]

ベースクラス: 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).

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:

$U1(\lambda = \pi) = Z$
$U1(\lambda = \pi/2) = S$
$U1(\lambda = \pi/4) = T$

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

condition_bits

Get Clbits in condition.

List[Clbit]

decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

definition

Return definition in terms of other basic gates.

duration

Get the duration.

label

Return instruction label

str

name

Return the name.

num_clbits

Return the number of clbits.

num_qubits

Return the number of qubits.

params

return instruction params.

unit

Get the time unit of duration.