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ZGate

class ZGate(label=None)

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

Matrix Representation:

Z=(1001)\begin{split}Z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}\end{split}

Circuit symbol:

     ┌───┐
q_0: ┤ Z ├
     └───┘

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

Note

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

RZ(π)=(1001)=Z\begin{split}RZ(\pi) = \begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix} = -Z\end{split}

The gate is equivalent to a phase flip.

0011\begin{split}|0\rangle \rightarrow |0\rangle \\ |1\rangle \rightarrow -|1\rangle\end{split}

Create new Z gate.


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

ZGate.add_decomposition(decomposition)

Add a decomposition of the instruction to the SessionEquivalenceLibrary.

assemble

ZGate.assemble()

Assemble a QasmQobjInstruction

Return type

Instruction

broadcast_arguments

ZGate.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

ZGate.c_if(classical, val)

Add classical condition on register classical and value val.

control

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

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

ZGate.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

ZGate.inverse()

Return inverted Z gate (itself).

is_parameterized

ZGate.is_parameterized()

Return True .IFF. instruction is parameterized else False

mirror

ZGate.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

ZGate.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

ZGate.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

ZGate.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

ZGate.to_matrix()

Return a numpy.array for the Z gate.

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