U1Gate

U1Gate(theta, label=None)

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:

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

Attributes

decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

definition

Return definition in terms of other basic gates.

label

Type: str

Return gate label

Return type

str

params

return instruction params.

Methods

add_decomposition

U1Gate.add_decomposition(decomposition)

Add a decomposition of the instruction to the SessionEquivalenceLibrary.

assemble

U1Gate.assemble()

Assemble a QasmQobjInstruction

Return type

Instruction

broadcast_arguments

U1Gate.broadcast_arguments(qargs, cargs)

Validation and handling of the arguments and its relationship.

For example, cx([q[0],q[1]], q[2]) means cx(q[0], q[2]); cx(q[1], q[2]). This method yields the arguments in the right grouping. In the given example:

in: [[q[0],q[1]], q[2]],[]
outs: [q[0], q[2]], []
      [q[1], q[2]], []

The general broadcasting rules are:

If len(qargs) == 1:
```
[q[0], q[1]] -> [q[0]],[q[1]]
```

If len(qargs) == 2:

[[q[0], q[1]], [r[0], r[1]]] -> [q[0], r[0]], [q[1], r[1]]
[[q[0]], [r[0], r[1]]]       -> [q[0], r[0]], [q[0], r[1]]
[[q[0], q[1]], [r[0]]]       -> [q[0], r[0]], [q[1], r[0]]

If len(qargs) >= 3:

[q[0], q[1]], [r[0], r[1]],  ...] -> [q[0], r[0], ...], [q[1], r[1], ...]

Parameters

qargs (List) – List of quantum bit arguments.
cargs (List) – List of classical bit arguments.

Return type

Tuple[List, List]

Returns

A tuple with single arguments.

Raises

CircuitError – If the input is not valid. For example, the number of arguments does not match the gate expectation.

c_if

U1Gate.c_if(classical, val)

Add classical condition on register classical and value val.

control

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

Return a (mutli-)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

copy

U1Gate.copy(name=None)

Copy of the instruction.

Parameters

name (str) – name to be given to the copied circuit, if None then the name stays the same.

Returns

a copy of the current instruction, with the name

updated if it was provided

Return type

qiskit.circuit.Instruction

inverse

U1Gate.inverse()

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

is_parameterized

U1Gate.is_parameterized()

Return True .IFF. instruction is parameterized else False

mirror

U1Gate.mirror()

For a composite instruction, reverse the order of sub-gates.

This is done by recursively mirroring all sub-instructions. It does not invert any gate.

Returns

a fresh gate with sub-gates reversed

Return type

qiskit.circuit.Instruction

power

U1Gate.power(exponent)

Creates a unitary gate as gate^exponent.

Parameters

exponent (float) – Gate^exponent

Returns

To which to_matrix is self.to_matrix^exponent.

Return type

qiskit.extensions.UnitaryGate

Raises

CircuitError – If Gate is not unitary

qasm

U1Gate.qasm()

Return a default OpenQASM string for the instruction.

Derived instructions may override this to print in a different format (e.g. measure q[0] -> c[0];).

repeat

U1Gate.repeat(n)

Creates an instruction with gate repeated n amount of times.

Parameters

n (int) – Number of times to repeat the instruction

Returns

Containing the definition.

Return type

qiskit.circuit.Instruction

Raises

CircuitError – If n < 1.

to_matrix

U1Gate.to_matrix()

Return a numpy.array for the U1 gate.

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