# U1Gate¶

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

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).

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.

Attributes

 U1Gate.decompositions Get the decompositions of the instruction from the SessionEquivalenceLibrary. U1Gate.definition Return definition in terms of other basic gates. U1Gate.label Return gate label U1Gate.params return instruction params.

Methods

 U1Gate.add_decomposition(decomposition) Add a decomposition of the instruction to the SessionEquivalenceLibrary. Assemble a QasmQobjInstruction U1Gate.broadcast_arguments(qargs, cargs) Validation and handling of the arguments and its relationship. U1Gate.c_if(classical, val) Add classical condition on register classical and value val. U1Gate.control([num_ctrl_qubits, label, …]) Return a (mutli-)controlled-U1 gate. U1Gate.copy([name]) Copy of the instruction. Return inverted U1 gate ($$U1(\lambda){\dagger} = U1(-\lambda)$$) Return True .IFF. For a composite instruction, reverse the order of sub-gates. U1Gate.power(exponent) Creates a unitary gate as gate^exponent. Return a default OpenQASM string for the instruction. Creates an instruction with gate repeated n amount of times. Return a numpy.array for the U1 gate.