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qiskit.circuit.library.ZGate

class ZGate(label=None)[source]

The single-qubit Pauli-Z gate (\(\sigma_z\)).

Matrix Representation:

\[\begin{split}Z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}\end{split}\]

Circuit symbol:

     ┌───┐
q_0: ┤ Z ├
     └───┘

Equivalent to a \(\pi\) radian rotation about the Z axis.

Note

A global phase difference exists between the definitions of \(RZ(\pi)\) and \(Z\).

\[\begin{split}RZ(\pi) = \begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix} = -Z\end{split}\]

The gate is equivalent to a phase flip.

\[\begin{split}|0\rangle \rightarrow |0\rangle \\ |1\rangle \rightarrow -|1\rangle\end{split}\]

Create new Z gate.

__init__(label=None)[source]

Create new Z gate.

Methods

__init__([label])

Create new Z gate.

add_decomposition(decomposition)

Add a decomposition of the instruction to the SessionEquivalenceLibrary.

assemble()

Assemble a QasmQobjInstruction

broadcast_arguments(qargs, cargs)

Validation and handling of the arguments and its relationship.

c_if(classical, val)

Add classical condition on register classical and value val.

control([num_ctrl_qubits, label, ctrl_state])

Return a (mutli-)controlled-Z gate.

copy([name])

Copy of the instruction.

inverse()

Return inverted Z gate (itself).

is_parameterized()

Return True .IFF.

mirror()

DEPRECATED: use instruction.reverse_ops().

power(exponent)

Creates a unitary gate as gate^exponent.

qasm()

Return a default OpenQASM string for the instruction.

repeat(n)

Creates an instruction with gate repeated n amount of times.

reverse_ops()

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

to_matrix()

Return a numpy.array for the Z gate.

validate_parameter(parameter)

Gate parameters should be int, float, or ParameterExpression

Attributes

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 gate label

params

return instruction params.

unit

Get the time unit of duration.

add_decomposition(decomposition)

Add a decomposition of the instruction to the SessionEquivalenceLibrary.

assemble()

Assemble a QasmQobjInstruction

Return type

Instruction

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(classical, val)

Add classical condition on register classical and value val.

control(num_ctrl_qubits=1, label=None, ctrl_state=None)[source]

Return a (mutli-)controlled-Z gate.

One control returns a CZ 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(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

property decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

property definition

Return definition in terms of other basic gates.

property duration

Get the duration.

inverse()[source]

Return inverted Z gate (itself).

is_parameterized()

Return True .IFF. instruction is parameterized else False

property label

Return gate label

Return type

str

mirror()

DEPRECATED: use instruction.reverse_ops().

Returns

a new instruction with sub-instructions

reversed.

Return type

qiskit.circuit.Instruction

property params

return instruction params.

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()

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(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.

reverse_ops()

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

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

Returns

a new instruction with

sub-instructions reversed.

Return type

qiskit.circuit.Instruction

to_matrix()[source]

Return a numpy.array for the Z gate.

property unit

Get the time unit of duration.

validate_parameter(parameter)

Gate parameters should be int, float, or ParameterExpression

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