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# U1Gate

class U1Gate(theta, label=None)

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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:

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

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(opens in a new tab)

Create new U1 gate.

## Methods Defined Here

### control

U1Gate.control(num_ctrl_qubits=1, label=None, ctrl_state=None)

Return a (multi-)controlled-U1 gate.

Parameters

• num_ctrl_qubits (int) – number of control qubits.
• label (str or None) – An optional label for the gate [Default: None]
• ctrl_state (int or str or None) – control state expressed as integer, string (e.g. ‘110’), or None. If None, use all 1s.

Returns

controlled version of this gate.

Return type

ControlledGate

### inverse

U1Gate.inverse()

Return inverted U1 gate ($U1(\lambda){\dagger} = U1(-\lambda)$)

## Attributes

### condition_bits

Get Clbits in condition.

Return type

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

Return type

str

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.